LAWS OF MOTION in ONE SHOT | All Concepts & PYQs | Basics to Advanced | Class 11 NEET

So let's begin our lecture, what is its name? Newton's Laws of Motion. You said, sir, what is force? I said, just a push or a pull. Either push or pull, end of story. Okay? Push or pull. Sir, what is this spring force? I said, brother, you must have seen it. For example, if I say appearance, we call this a spring. Okay? This is not an ideal spring. You said, suppose this is a pulley. A mass is hanging here. A mass is hanging here. And this is suppose tied up in this manner from above. So you will directly say, sir, look, if I say the tension in this rope is t. The tension in this rope is t. So in this it's t, in this it's t, so what will be the tension in this, my brother? Virtual Work Method. It's a very lovely method. Okay? With this, your many pulley-type questions will be solved in a snap, in one line. Please attend the lecture in a good manner. Hello, what's up, friend? So, continuing our series, let's move to our next lecture, which is named Newton's Laws of Motion. As often after the chapter ends, you people have the need, "Sir, where will we get the PPT of this lecture?" So, I will tell you that the PPT of this entire lecture will be available on our PW app. You go to the Google Play Store. Okay? Go to Android, go to iOS. There you will download the PW app, and there you will find many students studying for JEE and NEET. Okay? So, there you will find the PPT of this lecture, of this entire lecture that I am going to cover, the complete PDF will be available there. So, go and download it from there. First thing. Second thing, my brother, because it is obvious that by now we had completed three chapters. One was named Vector, the second was named Motion in a Straight Line, the third was Motion in a Plane. The next lecture is here, NLM. I am not covering friction in this. Otherwise, if I covered friction, the lecture would become very long. So, we are going to cover this without friction, and the friction part, I will cover in the next lecture, which will be Circular Motion. I am clarifying this to you beforehand. Circular Motion, because it is a small chapter, not a very long chapter, and it has a part of 3 hours, it finishes well within 3 hours. So, I will cover the friction part within that, so that that thing will be balanced there, and we will be able to cover both these parts in a proper balanced time, my brother. Do you understand what I am saying? Is it clear? So, let's proceed with the lecture now, and one more thing, my brother, if you wish, quickly join my Telegram channel. On this Telegram channel, I will also upload the complete PPT of this lecture. Besides this, I keep uploading many very important PDFs on this Telegram group. Okay? And do join it. So, let's begin our lecture, what is its name? Newton's Laws of Motion. What is Newton's Law of Motion? I said, brother, listen to me. Listen to the most important thing first. First of all, I will quickly give you a revision of Class 9th, which you used to study in Class 9th. You said, what? You said, sir, first of all, what is inertia? I said, inertia is a property due to which if a body is at rest, it will tend to remain at rest, and if it is moving with constant velocity, it will tend to keep moving with constant velocity in a straight line path. This tendency, this property, you can call it what? Inertia. You said, okay, brother. You said, meaning? I said, brother, the direct meaning is, you understand it like this, brother, this is some body. Yes, brother, it's a body. Is it at rest? Yes, it is at rest. So, it will tend to remain at rest. See, it is at rest. You said, yes, sir, it is at rest. It should remain at rest. This property, this tendency to want, we are at rest, so we want to remain at rest, no matter what. We will try to remain, it's a different matter that desire is not always fulfilled. It's not necessary that what I want always happens, okay? Or what you want always happens, it's not necessary. But it wants to be at rest, so it is at rest, so it wants to remain at rest. So, we call this property, my brother, inertia. I said, okay, brother, okay. Similarly, if it is moving with constant velocity, it will want to keep moving with constant velocity. So, I call this property, my brother, inertia. In Class 9th, we used to study this definition. Sir, what does constant velocity mean? I said, velocity means velocity is constant. Yes, sir. Direction is also constant. Yes, sir. Direction is constant, so the particle is moving like this, where the direction is constant. So, what can I say about this, brother? You said, sir, you can say the particle is moving in a straight line path. Obviously, man, the particle will move in a straight line. If someone's velocity is constant, then it will definitely move in a straight line path. You said, okay, sir. That's why they say that if a body is at rest, it will tend to remain at rest, and if it is moving with constant velocity, it will tend to keep moving with constant velocity. After that, the next term was momentum. You said, what is momentum? I said, it's just a formula, remember it, brother, mass * velocity. For now, remember this much. Actually, momentum is, it is the total net amount of motion contained in a system. How much motion does a system have? How will you find this out? You said, brother, we have defined a new physical quantity here. We said, brother, momentum, which is calculated by the formula mass * velocity. I said, okay, brother. It reminded me of inertia, sir, that the more mass a thing has, the more of this inertia property it will have, my brother. These are small theoretical points of yours. After that, we go to, sir, force. You said, sir, what is force? I said, just a push or a pull. Either push or pull, end of story. Okay? Push or pull. You can say. You said, yes, sir. If you want to finish the shortest definition of force, you will directly say, sir, push or what, my brother? Pull. I said, okay. Then we did a lot of observations. Many observations. Many observations. We saw various types of forces. We saw different types of forces that are acting in our surroundings, all around us. Among these, one is gravitation, another is friction. One is tension, one is normal, one is electrostatic, one is magnetic. We saw many forces. After that, we did one thing, we divided force into four categories, my brother. I have written it here. Just keep listening for now. These are things to listen to. Okay? We divided force into four categories, brother. First, gravitational force, like mg. Gml mm2 / r² is there. Okay? Okay, sir. We called this gravitational force. Sir, electromagnetic force. Electromagnetic force means, sir. Basically, we have kept categories within this: tension force, normal force, friction force, electrostatic force, magnetic force. For example, you see electrostatic force, it acts between two charges. Okay? Magnetic force, you see that, you will study that in 12th. You cover this thing in the 12th syllabus. But for now, understand this. Brother, all these forces, we have kept them under electromagnetic force. Because in these forces, somewhere, the charges within the atoms are involved. Okay, sir. Okay. You don't need to go into much detail here. Just glance over it. After that, there is strong nuclear force or weak nuclear force. We have divided force into these four categories. We don't study the third and fourth parts, strong nuclear force and weak force, at all. We study them briefly in 12th, for maybe 15-20 minutes, which is called nuclear force. Nuclear force means, for example, if you have seen the structure of an atom, there is a nucleus inside the atom. There are protons and neutrons inside the nucleus. Yes, sir. Protons have positive charge. So, in a very small space, so many positive charges are living together, which is an impossible thing. How can so many positive charges be in the same place? Positive repels positive. Positive repels positive. So, in fact, if there was only repulsion, the nucleus would explode. It wouldn't be stable. But even then, it is stable. So, it is obvious that there is repulsion between positive positive protons in the nucleus. But there must be some other force, let's call it a strong force, some other attractive force that has counterbalanced it, that has canceled it out. So, after more research, it was found that, sir, another force acts, which acts between proton-proton, neutron-neutron, and proton-neutron, my brother, it acts between the nucleons. So, we named it, what, my brother? Nuclear force. Okay? So, this means, sir, repulsion is happening. Attraction is also happening. So, attraction has, in a way, balanced that repulsion. So, well, all these things are not useful to you at all right now. I just explained them as they came up. What is useful to you now is, sir, numericals. Numericals in Newton's Laws of Motion. But before that, a little theory is necessary. So, let's study all the theory. After all these things, Newton gave us three laws. Okay, sir. Which ones, sir? First law. Sir, Newton's First Law. Sir, if a body is at rest, it will tend to remain at rest. Sir, this sounds like the definition of inertia. I said, yes, that's why it is also called the Law of Inertia. Newton's First Law is also called the Law of Inertia because the definition of inertia was: if a body is at rest, it will tend to remain at rest. And Newton's First Law says: if a body is at rest, it will tend to remain at rest, until when? Until an external force acts on it. It just added one line. Until when? You said, until an external force acts on it. Meaning, brother, this, suppose this is a body. Suppose this is a body. It is at rest, so it will tend to remain at rest. Until when? Until I push it. Until I pull it. See. I pulled it. So, see, it started moving. I started pushing it. So, brother, it started moving. So, if a body is at rest, it will tend to remain at rest. And similarly, if a body is moving with constant velocity, it will tend to keep moving with constant velocity. Until when? Until an external force acts on it. So, this is your Newton's First Law. Then comes Newton's Second Law. Sir, Newton's Second Law means F = ma. I said, no, Newton's Second Law is not F = ma. I am explaining this here very calmly. You said, sir, what is Newton's Second Law? Second Law. I said, brother, according to Newton's Second Law, you will directly say, Newton's Second Law. Brother, they said this: Sir, sir, the rate of change of momentum of a body is equal to the net external force acting on the body. Are you understanding? Let me repeat it. This is their statement, the statement of this law: The rate of change of momentum, rate of change of momentum means, differentiate p with respect to time. The rate of change of momentum of the body is called the net external force acting on the body. So, you will directly say, sir, Net External Force, if I ask you here, what will it be? So, you will directly say, sir, dp/dt. What can I write instead of p? I said, you can write mass * velocity. I said, okay. As soon as I open this, it will be m * dv/dt. I said, very good, brother. m * dv/dt + v * dm/dt. You said, is this understandable? You said, yes, sir, it is perfectly understandable. So, can I write it like this, sir, Net External Force equals, my brother, m * dv/dt + v * dm/dt? I said, correct. Now, after this, if I say that if mass is constant, if I say that your mass is, my brother? You said, sir, mass is constant. So, if you make mass constant, then dm/dt will be zero, because the differentiation of a constant is, my brother, zero. So, this means F becomes what, sir? m * dv/dt. And dv/dt is, my brother, acceleration. So, this means F = ma is not your Newton's Second Law. Newton's Second Law is this. This is just a special case of it, that if, suppose, mass is constant. When the mass of the system is constant. This means the mass of the system is not changing, then the net external force will be, brother, equal to m * a. Sir, for example? I said, example, like rocket propulsion. In rocket propulsion, smoke is continuously coming out. Fuel is continuously burning. So, this means I cannot apply F = ma directly there. Absolutely not. It will be wrong. This means for all variable mass systems, whose mass is continuously changing, like a trolley, rain starts falling on the trolley, raindrops start falling, and the trolley is moving forward. So, you cannot apply F = ma there. It will be wrong from there. Are you understanding? Okay, sir. Okay. But in Newton's Laws of Motion, in all such cases where mass is constant, you will directly say, F = ma. You can apply it there. Can you apply it? You will apply it. Okay, sir. This is your Newton's Second Law. Brother, all these things are written here. Sir, Newton's First Law, definition is written here. This screenshot of my book, I have taken it as it is. You can read it from here if you wish. Okay? Newton's Second Law. You said, Newton's Second Law, F_net_external = dp/dt. I have explained all these things here. Then comes, brother, Newton's Third Law. You said, Newton's Third Law means? I said, Newton's Third Law statement is: for every action, there will be a reaction. But this is not the complete statement. Listen to the complete statement: For every action, there will be an equal and opposite reaction. Okay, sir. But listen carefully. For every action, there will be a reaction, but it will happen at the same time, simultaneously, of the same nature, and it will be a two-body event. You said, what do you mean? I said, what I mean is, if you understand this carefully, feel it more than writing it. Get an understanding of it in your mind. You said, what? You said, if A applies a force F on B, then B will also apply a force F back on A. This is called Newton's Third Law. Although this is not the complete law. I will complete it now. If A applies a force F on B, then B will also apply a force F back on A. Equal and opposite, at the same time, simultaneously, direction opposite, two-body event. Meaning, A applied on B, then B also applied on A. One force is acting on A, and one force is acting on B. And one of its characteristics is that we cannot tell which is action and which is reaction. We cannot tell. If you call one reaction, then you have to call the other reaction. Are you understanding? So, these things, my brother, I have also written here, according to Newton's Third Law. You said, is it written here? You said, sir, for every reaction, there is an equal and opposite reaction at the same time, simultaneously, of the same nature. The nature should also be the same. Same nature means, suppose mg is gravitational. The action-reaction of mg will be mg. The action-reaction of tension will be tension. It's not that the action-reaction of tension will be mg. No, brother, same nature. Those four fundamental categories in which I had put F, I had put F into four categories: one is gravitational, one is electromagnetic, one is strong nuclear force, and weak nuclear force. So, it should be of that same nature. Meaning, suppose A applies a normal force on B, then B will also apply a normal force back on A. It's not that it will apply mg. Are you understanding? Okay, sir. Okay. After this, we talk about. These are our small Class 9th things, small small things. After this, well, there are some small questions on this. I will make one thing clear to you, student. We saw that, sir, F = dp/dt. I said, okay, brother. Now, small questions come in this. You said, p is given, brother, 3t² + 4t. Momentum is given like this. They will say, brother, tell the force. Okay? Tell the force, brother, what will be the force? You said, find force. Like this, the question will come. Find force. I said, okay, brother? Find force at t = 2 seconds. So, you will directly say. Oh brother, what will be the force? Oh brother, differentiate it, brother. Differentiate it. So, what will be the differentiation, brother? Sir, we will differentiate. F = dp/dt. It will write it completely properly. The particle is moving in the x-axis, so that it gives this momentum. You differentiate it. What will come? 6t + 8 will come. Put the value of t here. What will F be? It will be 12 + 8 = 20. They will give the mass, suppose they say the mass is 2 kg, so tell the acceleration. Now, here F = ma, because mass is constant. They will say, brother, what is the value of mass? You said, the value of mass is 2 kg, so tell the acceleration. So, you will directly say F = ma. Sir, F = 2. The value of mass is 2, so what will be the acceleration? It will come out to be 10. So,

Simple questions like these might be the first ones you encounter. After that, sir, there is an average force, and what is an average force? I said, brother, I said an average force is delta P / delta T, change in momentum divided by total time interval. This is called average force. You might get questions based on this. So, I will make one thing absolutely clear to you, beta, that you might be going through some book. You might be finding quite a few questions based on this. Questions on collision, collision, you might be finding quite a few. So, the collision, collision part, beta, I will cover in center of mass, collision. Are you understanding? I will cover the collision part in center of mass and collision. Is it clear? I will clarify one thing for you. Because, brother, if I tell you, brother, this particle came. This particle came. It came and collided here and went away after colliding. So, tell me, what will be the change in momentum here? So, brother, reading here and reading there doesn't make any sense, right? Now, talk only about force here. Talk about f = ma. Learn to apply Newton's law. Learn to apply f = maa. Learn the concept of pseudo force, learn the concept of tension, learn the concept of spring force, learn the concept of normal. Are you understanding? Learn all these things here. Okay? Learn how you have to play in inertial frames, non-inertial frames here. Okay? So, this part, which we will already study in collision, so I am not covering this part here. And in JEE, they don't cover this part. JEE covers this part in center of mass and collision. They don't cover it in Newton's laws of motion. Are you understanding? So, my brother, I will clarify this part beforehand. There should be no confusion in this. They say, we will do this, my brother, in center of mass and collision. We have to do it there. So, why read this twice? Okay? Okay, sir. And one more thing from here, sir, bring this here. So, what will dp come out to be? It will be f.t. I said, okay, sir, integrate both sides. So, what did we learn from here? They say, sir, the graph of f versus t, sir, the graph, the area of this graph, what will it give? They say, brother, it will give the change in momentum. Remember the area of the ft graph. It gives the change in momentum. They say, how did you know? I said, take dt to the other side. Sir, integrate this. Sir, sir, at t = t1, okay, suppose the momentum was p initial, at t2, suppose the momentum was p final. The integration of this came out to be p. So, p final - p initial will be delta p, which is basically fdt from t1 to t2. Are you understanding? Is it clear? I said, okay, brother, okay. So, basically, this is the story behind it, my brother. So, these are small things that you, this, will be absolutely clear in this. The collision part, we will cover there. The rest of the part, we are going to start here. So, after this, the important part that comes is forces. I said, okay. Now we have to study many forces here. For example, the first force is gravitational force. Suppose I placed a block here. Its mass is m. So, tell me, where will mg act on it? So, you have to apply mg downwards, towards the center of the earth. It acts downwards, towards the center of the earth. We see this in gravitation. We see in detail in gravitation why this happens. So, if I say that I have placed a block here, m, so it will act towards the center, my brother, like this, mg. I have placed a block here, m, so it is acting towards the center like this, my brother, like this, mg. Similarly, I have placed a block here, m, its mass is m, so towards the center, a force will act on it like this, my brother, mg. This is called gravitational force. I said, okay, brother. After that, the next one you have is a tension force. Tension force. I said, okay. They said, what is the meaning of tension force? I said, understand the meaning of tension force like this. Suppose there is a rope, and I have hung a mass here, of mass m. Okay, sir. So, if this rope were not there, would this mass m fall down? They said, yes, it would fall down. Who would make it fall down? They said, brother, mg force would make it fall down. I said, is this mass in equilibrium? Is the equilibrium broken? Net force is zero. Is this mass at rest? I said, yes. What force is acting downwards? mg. Even after that, it is at rest. It is in equilibrium. So, someone must have canceled it. Who canceled it? The rope. The rope. This means what did the rope do? It must have canceled this mg. The rope canceled this force. Now, what is the net force on this block? They say, sir, the net force is zero. So, if it is zero, then the downward force equals the upward force. So, someone applied a force upwards. Who applied it? The rope applied it. So, the force applied by the rope upwards, we call it the tension force here. What is the story behind this? They say, the story behind it is. There was your rope. You tried to hold it and pull it in a way. To increase its internal bond length, to increase its internal bond length. So, tension developed inside the rope. For example, I will give a small demo here. For example, if I tell you, this is not an ideal case, it is just enough for you to feel. If I tell you, like a spring, if I hold a spring and pull it like this. See, I pulled it like this. Okay? First, get the feel from this. As soon as I pull it, the spring was happy in its place. Happy in its place. It was saying, we are very happy here. We are perfectly fine here. Everything is going well in our life. You held it and pulled it like this. So, what did you do? You increased its bond length. You changed its length. You disturbed it. So, it wants to regain its old position, and to regain it, it is applying force on my hand. You will say, sir, I am not feeling it. I said, see, if I let go, it will go back quickly. So, in a similar way, you see a similar case inside the rope, that you are trying to hold the rope and pull it. So, the rope wants to regain its old position. And to regain its old position, the force it applies, what do we call it, my brother? Tension force. And what is the specialty of tension force? That is, sir, what kind of force is it? I said, it is a pulling force. It is a pulling force. Sir, it acts. It acts away from the body. It acts away. Very, very important part. It acts away from the body. It acts away from the body. Meaning, suppose you are making its free body diagram, then it will act away from it. It will act upwards. Sir, FBD means Free Body Diagram. I will come to FBD a little later. Okay? So, this means, sir, in which direction will the rope act on it? Away from the body, towards the rope. Write it completely. Away from the body, towards the string. They said, okay, sir. And, sir, how much will it act? Always away from the body, towards the rope. And what is its nature, my brother? It is a pulling nature. Are you understanding? Meaning, for example, a little later, if I give you a question like this, I say, brother, here is a block, and we have attached two ropes here. So, tell me, how would the rope apply tension on it? You will say, sir, sir, see, this is the block. Its mass is m. So, a force will be acting downwards, mg. Mg will definitely act. They said, yes. I said, here is a rope, so the rope is applying force. So, in which direction will it apply force on this block? You will say, sir, on the block, sir, whenever you apply force, act away from the body. This means the tension acting on it will be away from the body in this direction, like this, t1. Meaning, this rope is holding this block and pulling it in this direction. Similarly, this rope is holding this block and pulling it in this direction, like this. T2. Meaning, if I tell you, just make a block, and after making the block, tell me which forces are acting on it? So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property of normal force is that it acts towards the body. It acts towards the body. This, you made a video of the block, mg is acting below the block, so where will normal act? Towards the body. Towards the body, we have applied what, my brother, here? Normal. Perpendicular to the surface. Just catch this thing. Acts towards the body. See, understand it like this. Tension is outwards. Throw tension outwards. Tension must always be applied away from the body. Take normal inwards. Throw tension outwards. Take normal inwards. Like this, from here. This is the trick behind it. If, if you ever get confused, then. Like the next question. If I tell you, suppose this is an inclined plane. I said, okay. I have placed a block here, mass m. So, tell me, which forces are acting on it? You will say, sir, one will act downwards, mg. I said, okay. Sir, is this block in contact with this inclined plane? I said, yes. So, this means, towards the block, towards the body, what will be acting? Normal will be acting. Towards the block. Are you understanding? I said, okay, brother. Next part. They said, sir, if I talk about it from here, I said, what? They said, sir, suppose this angle is theta. I said, okay. This angle is theta. Suppose someone said, we have placed a sphere here. Now, tell me, how will forces act on it? I said, here, here, apply mg first, sir. Apply it exactly at the center, sir. Why do we apply mg at the center? We will see that later. For now, apply it at the center and understand for now that we are applying it at the center. Okay, sir. We will see the reason for this later. We will see the reason for this in center of mass, rotation. Sir, is it touching this? I said, yes. So, from here, what will be acting on it? Normal is coming. So, we show normal like this. Let's look at one more case. For example, if I tell you, suppose here I have two such spheres. I said, okay. And suppose I have placed two walls like this. Like this. Two walls like this. Like this, I have placed a ball like this, and this is the ground. This is the ground. I want you to make its FBD. Tell me which forces are acting on it? So, you will say, sir, one will be mg. I said, okay. Is this sphere touching this wall? I said, yes. So, from here, normal n1 will be acting. Is this sphere touching this wall? I said, yes. So, normal is acting from here, n2. Sir, why is n2 not applied here? Because normal acts towards the body. We are making the FBD of the body. We are showing which forces are acting on this sphere. So, on this sphere, normal will always be towards the body. So, if I tell you, I just want you to make a block and show me which forces are acting on the block. So, you will say, sir, see, one force is acting downwards, mg. I said, okay. One force is acting in this direction, T1, and one force is acting in this direction due to this rope, T2. Who applied this T1? This rope applied it on this block. Who applied this T2? This rope applied it on this block. Who applied this mg? They said, mg was applied by the earth on this block. So, these T1, T2, mg are three forces acting on this block. So, a diagram in which you are showing the forces acting on this block, that diagram is called a free body diagram. So, a doubt arises. They say, what is a free body diagram? I said, the meaning of a free body diagram is that the person whose free body diagram you are making, suppose you, suppose you are making the free body diagram of this block, so it means you are making the free body diagram of this block, so it means, tell me which forces are acting on this block. Tell me which forces are acting on this block. So, you will say, sir, T1 is acting, T2 is acting, and mg is acting. I said, that's it. The story is over. Okay? So, you, you have shown all the forces in one diagram. So, this is what we call a free body diagram. Is it clear, brother? They said, okay, sir. Similarly, there is a normal force. Okay, sir. Normal force. They said, sir, if, if two bodies are touching each other, then I can say that a normal contact force will act between them. Meaning, they said, sir, if a body is in contact with something, then a normal force acts. And the specialty of normal force is that it is a pushing force. It is a pushing force. And it always acts, it acts towards the body. It acts towards the body. And how? It acts perpendicularly. How does it act, my brother? Perpendicularly. They said, meaning, case, sir, example, meaning, I said, see how you understand with an example. Suppose I took a block of mass m and placed it like this. Okay, sir. Now, if I ask you to make the FBD of this mass m, tell me the free body diagram. So, you will say, sir, mg will be acting downwards. I said, mg will definitely be acting, brother. So, tell me, is it in contact with the ground? Yes, sir, it is in contact with the ground. So, from the ground, upwards, acting towards the body, there will be a normal force. The property

It seems like the text is a transcript of a physics lecture explaining concepts related to forces, equilibrium, and tension in ropes, using examples and problem-solving techniques. Here's the translation:

If it appears to be hitting at any angle, we will take its components. We will break it down. And we will say, if, sir, the particle is in equilibrium, then in the x-direction, the net force on it is zero. In the y-direction, the net force on it is zero, and in the z-direction, the net force on it is also zero. For example, let's start the question with very easy problems. Then, slowly, slowly, we will increase the level. We said, sir, suppose this is a 10 kg block, and it is in equilibrium. Actually, there's no need to say that. It's clearly visible. Otherwise, the rope would break. It's clearly visible, sir, that it is in equilibrium. So, sir, if it is in equilibrium, and I make the FBD of 10 kg, you will directly say, sir, mg is acting downwards. Sir, who has balanced it? I said the rope has balanced it. I said, okay, sir. So, this means the rope must have applied tension on it, and in which direction? Upwards. Sir, why upwards? Because I said tension is always away from the body. This means tension must have been applied upwards. Sir, it has to be applied away from the body. So, that means it is in equilibrium, so what will be the value of t, my brother? mg, and what is the value of mg? It's 100. Any problem? They said no problem. Next. The next part. They said, sir, if nothing is mentioned here, then the rope is massless. Remember. If nothing is mentioned, it means this string of yours is massless, my brother. Massless means either their mass is zero, or their mass is so little, so little, so little that you can neglect it. Now, if I ask you, I said, tell me the tension here and here. So, if you are asked to tell the tension here, what will be the tension in this rope? You will directly say, sir, tell me, sir, if you make the FBD of the block, how much mass will be pulling down, how much force will be pulling down? mg, how much? 200 Newtons. How much is acting upwards? Tension. So, this means tension will be equal to, sir? 200. Do you understand? It will be equal to mg. Similarly, if I ask for the tension in this rope, you will directly say. They said, sir, tell me, if I want to go individually, if I make the FBD of 10 kg. I said, okay, brother, make the FBD of 10 kg. So you will directly say, sir, call this t2, call this t1. Sir, there is a rope above, so tension will act upwards, t1. Sir, due to mg, a force of 100 Newtons will act downwards. I said, okay, sir. And a force will be acting downwards, another t2. Another force will be acting downwards, my brother, how much? They said t2. They said why is t2 acting downwards, sir? Oh, my brother, this rope is also below, isn't it? Tension t2 has developed in this rope, so it is obvious that you can see the block, yes, the block is visible. The rope above is visible, so show the tension upwards. The rope below is visible, so show the tension downwards, and mg is also acting. Now, if I ask you, is this block in equilibrium? They said yes, sir, it is in equilibrium. So, if it is in equilibrium, then what will I write? Sir, equilibrium means the upward force equals the downward force, t1 = mg + t2. And what is the value of t2? It's 200. So, as soon as you put 200 here, sir, it will come out to be 100 + 200, which will come out to be 300. You will call this a very basic fundamental problem. You don't need to solve such problems like this anymore. I will tell you a great method for this. What? I will call it the scale-type method. Okay? Scale-type method means I said, you do one thing, you hold the rope from here. Hold the rope here. If you hold the rope from here, then I know how much total mass is being held below? So, you will say 20 kg. So, you are holding 20 kg of mass. So, this means the mg of 20 kg is how much? 200. So, this means the tension here will be 200. If I ask you, I said, tell me here, here, here. Hold the rope from here. As soon as you hold the rope from here. To hold 20 and 10, 30 kg of mass, how much force? How many Newtons of force will be required? 300 Newtons. Done. Basically, you can see it like this, in all these problems, in all these questions, they are in equilibrium. You do one thing, look at the total mass hanging below the rope. Multiply it by g. For example, if I ask you, sir, tell me the tension here. I said, the tension here, below it is 30 kg, so 300. Sir, tell me the tension here. How much total mass is hanging below? 50 kg, so 500. Tension here. They said, brother, how much mass is hanging below? 30, 20, 50, and one 60. 600. Done. Are you getting it? Sir, these are massless ropes. What if they give a massive rope? I said, then no problem, we will solve it by treating it like a block. They said how? I said, look here, if I ask you a question here, there is a rope. This time I have given the rope a mass of 10 kg. See, the rope given before was massless. Sir, the rope was massless. What does that mean? I said, point A, point B, point C. Sir, this means that in these problems, we can write tension at A = tension at B = tension at C = 100. I said, okay. But here, as you go upwards, the mass hanging below keeps increasing, so the tension will be different at different places. For example, if I ask you, I said, brother, this is point A, this is point B, this is point C. I ask you, what will be the tension at this point? You will say, it's 10 kg, so how much mass will be acting downwards? 10 kg? It will be 100. Are you getting it? Okay, sir. I ask you, tell me the tension at B. What will be the tension at B? So what will you say, sir? It's 10 kg, and 5 kg. Why this 5 kg, sir? The total mass of the rope is 10 kg, so the mass of half of it will be 5 kg. So, 10 plus this 5, how much is it? 15. So, brother, how much tension will come due to 15 kg? 150. I ask you, tell me the tension at C, at the topmost point. You will directly say, sir, look, the mass of 10 kg is this, the mass of 10 kg is this, the total mass is 20 kg, so 200 Newtons will be acting downwards. Are you getting it? Clear? This means you just look at the point where the tension is being asked, multiply the total mass hanging below it by 10. Next question, do both questions now. All students, show the tension at A, B, C, D, E, F. Quickly. Pause the screen. You are watching. Pause the screen quickly. Let's see. Sir. I said, yes. Sir, tension at A, sir, tension here. Sir, this, sir, this is a 10 kg string. Okay? So how much mass is hanging below it? 20 kg, so 200. Sir, tension at B, tell me, how much is hanging here, sir? 20 is here, and 5. Sir, the total mass of the rope is 10 kg. This is the midpoint. I haven't written it, but I will mention it here. This is the midpoint, which means it is 5 kg, and this is 20 kg. So, total is 25 kg. Into g. Okay, sir. What will be the tension at C? I said, tension at C. I said, tell me this, it's 10 kg, this is 20 kg. So, this will be your 300. 300 Newtons. Okay, okay, sir. Sir, what will be the tension at D, my brother? If you look at the tension at D, yes, then see, 20, this 10, 30, and 10, 40. Total 40 kg of mass is hanging below. mg. And here, brother, here also, below this is 40, below this is also 40, below this is also 40, because this rope is massless, so its mass is approximately zero. If I ask you, tell me the tension at point E, what will you say? Sir, the tension at point E is, sir, 0 + 10 + 10 + 20. So, this means you will neglect its mass. That means the tension at D will be the same as the tension at E, my brother. And the same will be the tension at F. This is how these problems are solved. Similarly, if I ask this question, you will solve it very easily. They said what? I said, look, brother, this rope is massless. So, tension at A = tension at B = tension at C will come out to be 200. I said, okay, sir. And if we talk about tension at D, then you will directly say, sir, 20 and 10, 30, 300. I said, okay, sir. If we talk about tension at E, then you will directly say, sir, this is 5 kg. 10 and 5, 15. 15 and 35. So, this means it will be 350. And if I ask you the tension at, you will say 20 and 10, 30, 10 and 30, 40. This will come out to be 400. Are you getting it? Clear? So, these are your problems. I said, okay. It's possible that they might place it on an incline. A small problem. Placed on an incline. Now tell me. I said, placed on an incline, so what? Make the FBD. What will be acting here? Sir, tension will be acting here. And which force will be acting here? Sir, mg sin theta will be acting here. This means tension will be equal to? They said, sir, tension will be equal to mg sin theta. Sir, how did this mg sin theta come? I said, look at it once, because this will be used by you at least 1000 times in the entire physics. If I say that this angle is theta, and suppose I said that there is a block here whose mass is m, a particle whose mass is m, placed on an inclined plane. Then you will say, sir, look, if I make its FBD, a force will be acting downwards. I said, which force will be acting downwards? You will say, sir, mg will be acting downwards. I said, okay, sir. Okay. So, sir, if I take the components of mg, how? Sir, perpendicular to the incline and along the incline. Perpendicular to the incline and along the incline. If I take the components, then perhaps you will see this. They said what? Sir, this is theta. So, sir, pay close attention to this. Pay close attention, everyone. Okay, sir. This angle is theta. So, this angle is 90. So, this angle will be 90 - theta. Okay? So, this angle will be theta. Why? Because this line is perpendicular to it. Now, look carefully. Sir, how much force is acting here? I said, mg. So, brother, mg is acting here. So, the component of mg here will be mg cos theta. So, you will directly say from here, sir, the component of mg here will be mg cos theta, brother. Okay, sir. mg cos theta here. So, perpendicular to this, how much will be here, my brother? Sir, mg sin theta will be here. mg sin. Are you getting it? Clear? So, my brother, questions are asked in this manner here. Clear? I hope you have understood this. mg is acting, so mg cos theta, and here mg sin is acting. I have explained it once, and it is used very often. Okay? On this basis, here is another question for you. Okay? This is a very standard problem. You might get to see it many times here. What? They said, sir, the block, the particle, this small particle, is in equilibrium. So, tell me the theta and the force. Okay? Okay, sir. Sir, what does equilibrium mean? I said, equilibrium means net force is zero. Sir, what does net force being zero mean? I said, upward force equals downward force, rightward force equals leftward force. So, net force is zero, but only when you know which forces are acting. They said, yes, sir. So, this means, first of all, I will shift it a little to the side. First of all, why don't we find out in this problem which forces are acting? They said, yes, sir, tell me, sir. So, if I make the FBD right here, then will a force mg be acting downwards due to 6 kg? Yes, sir, you are right. Sir, there is a rope here, so there is a rope, my brother. So, can I say that tension is acting here, t? Yes, brother, that's absolutely correct. Tension t is acting here. That's absolutely correct. Tension t is acting here. mg is downwards. Tension t is acting here. So, are these three forces? Yes, sir, three forces. Is the body in equilibrium? So, where is it, brother? It's given. Yes, sir, the body is in equilibrium. Sir, okay, sir, you are saying the body is in equilibrium. So, can I say that if the body is in equilibrium, then the upward force equals the downward force? Rightward force equals leftward force? Clear? So, we have seen such problems in vectors as well. How did we used to solve such questions? First, we used to break all vectors into x and y. So, tell me this, sir, let's consider this as vertical and this as horizontal. This force is already broken down. No need to break it. This force is already downwards. No need to break it. Do I need to break t here? They said, yes, sir, absolutely. I said, so, brother, break it. Come on, quickly. If I make its FBD here, you will directly say, sir, look, one force is acting downwards, mg. Here it is. I said, okay, sir. 6 Newtons. Sir, one is acting this way, tension t. I said, okay. So, tell me, if this angle is theta, then will this angle also be theta? Ah, absolutely correct. Now, look. Tension is acting here, t. So, what will be the component of t upwards? t cos theta. And what will be the component of t backwards? t sin theta. So, can I say? I said, yes, brother. Sir, what will be the component upwards? t cos theta. What will be the component this way? t sin theta. So, from here, you can directly write, sir, t cos theta will be here, and my brother, t sin theta will be here. Now tell me, is it in equilibrium? They said, yes, it is in equilibrium. So, this means the forward force equals the backward force. Sir, how much force is acting backwards? t sin theta will be equal to, sir? It will be equal to 60. Okay, brother? Or not 60, I will write it as f. It will be equal to f. 60 backwards. And sir, the upward force, t cos theta, will be equal to, my brother? It will be equal to the downward force. What is its value, brother? Oh, 60, is it 60? Oh, ho, ho, ho. Okay, brother. Let's do one thing, let's not take 60. Let's take 8 kg. Okay? Otherwise, the angle will be 45 degrees. Okay? I have taken this as 8 kg, so a force of 80 Newtons will act. I said, brother, this will be acting, how much, my brother? If I take an 8 kg block, then the value of mg will be 80. So, you will directly say here, sir, this will come out to be 80. So, if I take its ratio, then tan theta will come out to be, sir, f / mg. Are you getting it? What will come out, my brother? f / mg. I said, okay, sir. What is the value of f, brother? Sir, the value of the force, sir, is how much? 60. And sir, what is its value, my sir? It's 80. So, 3/4. So, theta will come out to be 37 degrees. And if you put the value of theta here, then the tension will come out to be 100 Newtons after solving. Are you getting it? You can also say 100 Newtons tension like this. How? Sir, tell me, how much force is acting this way? 60. How much is acting downwards? 80. 60 is acting this way. 80 is acting downwards. Sir, are 60 and 80 both perpendicular to each other? I said, yes, brother, both are perpendicular to each other. So, sir, if both are perpendicular to each other, then can I say that their resultant will be 100 Newtons? I said, okay, the body is in equilibrium. So, can I say that the resultant of this 60 and 80 will be 100, and this 100 is being taken by this tension? This tension has cancelled out that 100. This means the value of tension will be 100. Are you getting it? Clear? So, this, my brother, is how such problems are asked. Okay. There is also a theorem for this, which is called Lami's Theorem. Look at that once. Okay? What does Lami's Theorem say? They said, sir, suppose three forces are acting on a particle. This is the particle. F1 this way, F2 this way, and F3 this way. Sir, the angle with F1 is theta1, the angle with F2 is theta2. The angle with F3 is theta3. I said, okay. If three forces are acting, not two, not four, not five. If only three forces are acting. The sum of f1 + f2 + f3 is zero. This means three forces are acting, and the particle is in equilibrium. Then we can apply this theorem. And this theorem says, my brother, what? F1 / the angle opposite to it, sin theta1 = f2 / the angle opposite to it, sin theta2 = f3 / the angle opposite to it, sin theta3. These three become equal to each other. Although I would not call this theorem very good. Okay? Because it is used less in physics, but it was my duty to tell you. I have told you. What is the limitation? Sir, the particle must be in equilibrium. If it is not in equilibrium, then we cannot apply this. What is the second limitation, sir? There must be three forces. If there are two forces, do not apply this by mistake. Are you getting it? Okay, sir. Yes. Okay. So, sir, sir, if we apply this here, then I said, now this is your homework. You do this problem. I will show it here once. How would we get the answer from Lami's Theorem? Look carefully. The answer comes like this. Sir, look. I said, yes. Sir, this is a vertical line. Like this. I said, okay. And this is also a vertical line. Like this. Okay, sir. So, let's say this angle is 90. This angle is theta. So, this angle will be 90 + theta. And again, this angle will be, sir, this will be, sir, 180 - theta. You check it. You have to do some calculation. Okay? After this, you will say, oh, sir, it's a very bad method then. Okay, I have to do all this. I said, yes, brother, okay, but check how it is coming. Okay, okay, sir. How is it coming? They said, the total sum should be 360. Okay? From there. So, now, if you want to write the statement, you can write it. What will you write, sir? Tension divided by the opposite angle with sin, equals the angle on this side divided by the angle on that side. The angle opposite to this one, which one, brother? 180. So, sin 180 - theta equals 80 / sin 90 + theta. You solve this. Your answer will be the same. First, solve these two. Look, I will solve it. First, solve these two. How much is it? 60 / sin theta. What is this? 80 / cos theta. Take this to the other side. Take this to the other side. Sir, sin theta / cos theta becomes tan theta. Tan theta = 60 / 80 = 3/4. Same answer. My first was to tell you once. Now, after this, it's your choice. If you feel like it, apply it. But I would suggest you learn this: brother, take the components of the force. Upward equals downward, rightward equals leftward. On this pattern, here is another question you will see in the market, in your modules everywhere: Suppose I have placed a 10 kg block in this manner. Okay? And I am asking in the question, find the force applied by the inclined plane. Force applied by the inclined plane. On the sphere. How much force did the inclined plane apply on the sphere? This means I want to know the value of the normal reaction here. Normal reaction will be acting from here. I said, yes, brother, you are absolutely right. Normal reaction will be acting from here. So, look carefully, how to find it? I said, brother, come, brother, how to find it? Look carefully. They said, sir, make the FBD. I said, absolutely, make the FBD, brother. So, tell me one thing, first of all, can I say that normal is acting from here, like this? Yes, sir, it is definitely acting. Sir, whose FBD am I making? I am making the FBD of this sphere. I am not making the FBD of the inclined plane. I am making the FBD of this sphere. Okay, sir. Okay. Sir, one normal is acting, sir, from here. Like this, like this. I said, you are absolutely right. Let's say, brother, this is n1, and this is your n2. And sir, below, who is acting? Sir, mg is acting below. Sir, this sphere is touching at two places. It is touching at two places horizontally, with this wall and with that wall. It is touching at both places. This means it is certain. They said what is certain? That sir, here, there will be two normals. It is touching at two places, and mg is acting below. So, three forces are acting. They said, how to do it? I said, now do one thing, break the forward force, backward force, this force, rightward force, leftward force. You just do the components. Okay? So, first, I am slightly erasing this inclined plane. Otherwise, all your attention will be on this inclined plane. If I remove it, perhaps you will see the sphere here. Otherwise, you won't see the sphere. So that you can see the sphere even better, I am also filling color in it. I will fill such color. Like this. Here, brother. Okay? Now, sir, tell me how to do it? I said, brother, look, the straightforward way to do the problem. They said what? Have you made the FBD? Yes, guru, FBD is made. Now, sir, tell me, normal m1 is acting this way, normal m2 is acting this way, and below, who is acting, my brother? Sir, mg is acting below. I said, okay, sir. Who is acting below, brother? They said, sir, mg is acting below. I said, okay, sir, mg is acting below. So, what to do? Break all the forces into x and y. Break all the forces into x and y. So, they said, okay, sir. Sir, look, I have put m * g below. I said, okay. Now tell me, break it into x and y. Sir, this angle is 37, this angle is 90, so this angle will be 53. Sir, this is 53, this is 90, so this angle will be 37. Any problem? They said, no problem. Now, tell me, sir, who is acting this way? n1. What will be the component of n1 forward? n1 cos 53. n1 cos 53. Okay, sir. One component will go upwards, how much? n1 sin 53. I said, okay, brother. What will be the component of n2 this way? n2. The component of n2 backwards will be n2 * cos 37. Can I say that the block is moving forward? Is it moving forward? No. So, forward force equals backward force. What is the component of n1 forward? n1 cos 53. What is the component of n2 backwards? n2 cos 37. Will these two be equal? The forward force, the backward force. Yes, sir. Why? Because mg is downwards. The force of mg is downwards, isn't it, brother? The force of mg is downwards. Okay? So, this means mg has no component in the horizontal direction. The forward force is the backward force. Okay, sir. So, will an equation come from here? Yes, sir, an equation has come. And one component of n1 will go upwards, and one component of n2 will also go upwards. Sir, what will be the upward component of n1? n1 cos 53. I said, okay, brother. Plus, sorry, it will be sin, not cos. n1 sin 53 + n2 sin 37. Sir, what will this be equal to? I said, upward force equals downward force. And who is the downward force? It will be equal to mg, which is how much? Are you getting it? I will say, do it like this. Problems are solved very easily. In Lami's Theorem, you will have to shift this vector forward. You will have to shift it here. You will have to shift it here. Then you will look at angles and all. Okay? Where the angle is going. Okay? So, there are chances of mistakes. I will say, do it directly. Here is n1, right? So, one component of n1 will be n1 cos theta. Here is n2, right? Component of n2 backwards is n2 cos theta. Sir, one n1 sin theta and one n2 sin theta. Upward force equals downward force. Rightward force equals leftward force. Done. Now, solve it. After solving, the answer here will probably be, look, n1 will be 80, and n2 will be 60. Solve this. And there is also a small trick to solve such problems. In four options, you can also do it by option elimination. How? They said, sir, tell me. Sir, this part is tilted very little. This part is tilted very little. This means this is, obviously, in a way, it is pushing it more. Are you getting it? Understand it like this. Understand it like this: suppose I place a sphere here like this, and place it on an incline like this. Then you tell me yourself, which one is bearing more weight? Which one is bearing more weight? Do you understand what bearing weight means? Place it on a skull, on someone's head, and place someone like this on their head, like this. Then on whose head is more weight falling? On this skull. Okay? So, from this, one thing will be sure, they said, what is sure? That sir, here, n1 has to be larger because the angle is smaller. 37 degrees is a smaller angle. This means it is like this, not like this, and this will be a bit more. This angle is not equal, it is different. So, this means here what has happened? It is 37 degrees. So, it is more downwards. So, more weight is falling on this skull. This means the value of n1 will be more. So, out of the four options, if you see that the value of n1 is the highest in one option, then tick that. Okay? And secondly, because the mass is 10 kg, and these angles are given as 37 and 53. This means the values of n1 and n2 have to be 60 and 80. They have to be 60 and 80. Why 60 and 80? Because this angle, my brother, this angle is given to you as 90 degrees. This angle is 90 degrees. This angle is 90 degrees. Therefore, therefore, it is 90 degrees. So, brother, the resultant of 60 and 80 is 100. It matches perfectly. Are you getting it? And if not, my brother, if the problem does anything tricky, changes anything slightly, do nothing. Take the components. Forward force equals backward force. Rightward force equals leftward force. Clear? Note it down quickly, brother, before a minute passes. Okay? Now, let's look at one or two questions on this that are commonly found in books here and there. Okay? So that once you see these problems, your fear of these questions will disappear. For example, in this question, it is stated that the entire system is in equilibrium. The mass is 30 kg, and three ropes are given like this. Find the tension in each string. In this problem, it is not stated anywhere that it is in equilibrium. You have to use a little common sense. Brother, obviously it is coming.

The mass is obviously hanging here. It is not going forward, nor backward. This means it is indeed at equilibrium. Although it would have been better if equilibrium was written, but since it is not written, it is fine. So, how to do it now? Watch carefully. He said, "Sir, the best way to solve such problems is to not get caught up in side issues. Directly draw the free body diagram (FBD) of this person." This person. I said, "Okay, brother." Okay. "Sir, who is this?" I said, "Whatever you consider this to be, call it a node, or consider it a small point you've grasped." Okay. "Okay, sir." "Sir, there is a rope here, so there will be a force TA acting here." I said, "Okay, brother." "Sir, there will be a force TB acting here." I said, "Okay." "Sir, a force TC will be acting downwards." All three are three ropes. All three ropes are different. So all three TA, TB, TC will act. I said, "Okay, brother." As soon as you solve it and draw the FBD. "Sir, which force will be acting here?" T. "Sir, which force will be acting here?" TB. I said, "Okay." "Sir, TC will be acting downwards. But I would like you to write directly that 300 is acting downwards." He said, "Why are you saying 300, sir?" "Oh brother, isn't this at equilibrium?" "Yes, sir." "So, if 300 is downwards, then the tension will be 300." Keep this in mind too. This is not 300 kg. It is 300 Newtons. Okay? This means it is 30 kg. 30 kg means the weight acting downwards, mg, will be 300 Newtons. So, they have also shown it in the diagram. So, do not consider this as 300 kg. He has directly given the value of mg. Okay? So, I would say, you can directly put its value here. Then he said, "Now the problem is solved. There is no difficulty left in the problem. What do you need to do now?" "Sir, just draw the FBD, FBD." "Sir, tell me, sir, our FBD is drawn. Do we need to take components or anything?" "Sir, what is this angle?" 37. "So this angle will also be 37." You will directly say, "Sir, sir, what will be its component acting forward?" "Sir, TB cos 37 will act forward." "What will act upwards?" "Sir, TB sin 37 will act upwards." I said, "Okay, brother. The upward force equals the downward force." So you will write TB sin 37 is 3/5, which is equal to 300. This cancels out with three, so TB comes out to be 500. And if the value of TB is 500, then this will be 500 * 4/5, which will be 400. Clear. Who will be 400? This 400 will come. So TA, you can write TA will come out to be 400 by putting the value. Okay. Let's look at one more question on this. Suppose they have given a question of this type. They said, "Watch carefully." "The breaking strength of a string connecting wall and B is 175 Newton." This means, what is the maximum tension it can have? It can be 175, at most. If you apply more than this, the rope will break. I said, "Okay." "Find the magnitude of the weight of A." He said, "Okay, brother." "Tell me its weight. That is, its mass." Okay? Okay. "For which the system will be stationary." And what is the weight of B? Block B weighted 700 Newton. Okay? "Okay, sir." Okay. "So, brother, tell me one thing. Sir, tell me here. Directly, the tension is acting here." I said, "Okay, brother. Since there is a rope there, a tension will be acting, sir. Let's call it t1. So, let's say it is t2. And sir, which force is acting here? Sir, t3 will be acting here." So, basically, either you draw the FBD of each one individually. Or you use a little common sense. He said, "What common sense should we use?" I said, "Brother, tell me one thing. What is the maximum tension it can have?" He said, "Sir, it is 175." "The tension acting on it is downwards, mg. The normal force acting upwards. Both cancel each other out." If it is stationary, if you draw its FBD, then tension T will be acting backward. Which one, sir? The t1 one. So, tension t2 will be acting forward. I have named this t2. Obviously, brother. What is this mass doing? It wants to go down. That's why tension has developed here. This rope has also stretched. This rope has also stretched because the mass wants to go forward. And it is tied here, so it means the mass is not going forward anywhere. Okay? "Okay, sir." Okay. "So, if I ask you from here, sir, draw its FBD." "Brother, what force is acting forward?" T2. "What is acting backward?" T1. "T1 can be at most how much?" "Sir, 175." "So, it is directly understood, isn't it? To make it stationary, the tension in this will be the same as the tension in this." If the maximum tension in this is 175, then take the maximum tension as 175. Now he said, "Now, let's take this node O." "Sir, a tension will be acting here." "And T2 will be acting here." "We know the value of T2, how much is it, my brother?" 175. "Sir, let's assume the tension here is T3. And sir, mg will be acting downwards." "And sir, this angle is given as 30 degrees." The problem is solved. Are you getting it? The problem is solved. Okay? Now, let's see. You only need mg. So, what will you write? "Sir, a component of T3 will go forward, and a component will go upwards." "Sir, t3 sin 30 will go upwards, which will be equal to mg." "Sir, t3 cos 30 will go forward, which will be equal to 175." As soon as you take the ratio of both, tan 30 will be 1/√3, which will be equal to mg / 175. This means 175 will go to the other side. So, your tension will come out to be mg will come out to be 175 / √3. This is a very simple question. You have to deal with these questions in this way. Did you understand? Clear? If you want to note it down, brother, you can note it down quickly. So, let's move on to the next part, which is called the pulley system. Brother, you must have seen pulleys everywhere. Right? It has another name, Atwood machine. "Sir, what is a pulley?" And which pulley? We study the Atwood machine. Atwood machine. I have put its appearance here, my brother. Okay? I have taken a photo from the SKC book as it is to save time. Okay? So, you must have seen this in real life. Okay? We call this, brother, a pulley. But this pulley is a real pulley. Real pulley means what we actually see in real life. The pulley we are going to study in Newton's Laws of Motion is not a real pulley, it is an ideal pulley. Okay? That is, the pulley we will study in this chapter, its appearance is similar to these. Okay? But it is not actually this. "Sir, what is it actually?" I said, "Brother, I'll come to that." What is it actually? Let me repeat once more. This is our real pulley. This is our real-life pulley that we often see here and there. That we often use in our daily lives for big tasks. This is our real pulley. We will study this pulley in rotational motion. What we are going to study in Newton's Laws of Motion, the pulley we are going to study in Newton's Laws of Motion has some characteristics. He said, "What characteristics?" I said, "First of all, what should that pulley be?" "It should be massless." "What should it be, my brother?" He said, "Sir, the pulley we are going to study in Newton's Motion should be massless." "It should be massless." He said, "Massless means?" I said, "It should have no mass." Brother, it's impossible for something to have no mass. Okay? But you say, "Sir, it has mass, but it is very little." Very little. Or, by massless, we will make its mass, my brother? We will neglect it. I said, "Okay, brother." "And tell me more, sir." "Sir, the second thing is that there should be no friction between the rope and the pulley." Okay? Although we haven't studied friction yet. We study friction after NLM. Okay? So, you can easily remember this as well, that sir, we haven't studied friction yet, we will study friction later. Okay? So, you can recall it like this: there should be no friction between the pulley and the rope. That means, this rope, there should be no friction between it and the pulley. It means it should be completely smooth and flat. This means that the rope here, it slides over the pulley. He said, "Okay, sir." "And tell me more, sir." I said, "There is one more important result." He said, "What?" I said, "Suppose I take this case." "Understand carefully." "I am talking about this case right now." "If I draw its diagram, suppose some mass is hanging downwards." "And here also some mass is hanging downwards." I said, "Okay, brother. Both sides have masses hanging." So, my point is that sir, its mass, the mass of the pulley, the mass of the pulley is zero because it is massless. The pulley we are going to study in Newton's Laws of Motion is massless. It has no mass. I said, "Okay." "So, now if I draw its FBD, suppose brother, the rope is one, this is one rope. This rope goes like this and wraps around it." So, let's assume the tension on this side is t1, and the tension on this side is t2, suppose. Okay, sir. Okay. "And suppose the tension upwards, what do I say, my brother?" "Upwards, the tension is t3." I said, "Okay." "So, now if I draw its FBD, what will you say directly?" "Sir, what force is acting upwards?" I said, "T3 is acting upwards." "Sir, what force is acting downwards, my brother?" "T1 is acting downwards, and what else is acting downwards, sir?" "T2 is acting downwards, and what else is acting downwards, sir?" "And mass of the pulley * G is acting." "And the interesting thing is that sir, we have called the mass of the pulley what?" He said, "Sir, we have called it zero." Because your pulley is massless. Are you getting it? First. And second, sir, we will study this in rotation. There is no friction between the pulley and the rope. And the pulley is massless. That's why we will study in rotation that t1 becomes equal to what, my brother? t2. "Sir, the tension here, sir, if you are drawing its FBD." "Sir, if the tension downwards is t, then the tension here, sir, will also be what?" "It will be t." "Sir, why is the tension different?" I said, "We will study that in rotational motion." I'll just give you a slight idea. If the tension becomes different, then there will be a net torque about the pulley. And if there is torque, then brother, torque equals I alpha, which we study later. So, from that, i will come, and from that, alpha will come, whereas alpha should not come. Okay? Why should it not come? We will study all this in rotational motion. For now, just understand this much here. He said, "Sir, what?" I said, "Brother, if I talk about this, if this is one rope, then in this rope and in this rope, if this pulley is ideal, then your tension on this side and on this side will be the same, my brother?" "Sir, the tension will be the same." That means, I am trying to say here that sir, t1 = t2 = t. Let's assume, suppose. So, you will say directly, "Sir, what will t3 be equal to?" I said, "t1, the value of t1 is also t, and the value of t2 is also t." So, what will t3 be equal to? 2t. Are you getting it? In short, in short, now I want to say that suppose this is the pulley. Now, remember, you have to remember this, brother, from today onwards. He said, "Suppose this is the pulley." "One mass is hanging here." "And another mass is hanging here." "And suppose it is tied upwards like this, or it might be moving." It might be moving. So, you will say directly, "Sir, look, if I say the tension in this rope is t." "The tension in this rope is t." "Then what will be the tension in this, my brother?" "Sir, the tension in this will be 2t." You have to try to catch this pattern. tt 2t tt 2t. This pattern you have to try to catch. What is this, sir? He said, "Sir, you mentioned t as tension, but in books, they show it in some other form, don't they?" I said, "Yes, in books, they show it in some other form." Let's talk about the book's story. Look, if I talk about this, this mass hanging here, draw its FBD. So, when you draw the FBD of this mass, you will show tension upwards. Tension is always away from the body. I said, "Okay, brother." Okay. "So, this thing, this thing is drawn like this in books." Like this, t is written. So, understand that we are showing tension on this mass. And if I talk to you, "Brother, tell me the tension on this mass." "It will be upwards." So, you will show it like this, t. "Okay, sir." "If I draw the FBD of this pulley, then there is a rope on this side, and there is a rope on this side." "So, it means the tension here will be t." "Tension is always away from the body." "So, for the pulley, the tension will be downwards." "And if I talk about this side, then for this, the tension will be in which direction, my brother?" "For this also, the tension will be in which direction?" "Downwards." Are you getting it? "Okay, sir." "So, this t, this t, so this is 2t." "This means, sir, draw the FBD of the pulley. So, what is upwards?" "The rope is upwards. So, the tension acting upwards will be how much, my brother?" "It will be 2t." So, you have to catch this. If the tension in this rope is t, and the tension in this rope is t, then what will be the tension in this rope, my brother? "It will be 2t." Are you getting it? Clear? Catch this point. Because the pulley we are studying, what are we going to study, my brother? We are going to study the NLM pulley. In which we see. There are three things here, brother. Out of these three things, you just have to remember one thing. "Sir, what are the things in NLM?" I said, "First, its mass should be zero." Okay? Massless pulley. Mass zero means it should have very little mass that you can neglect it. Second, sir, friction. There should be no friction between the pulley and the rope. Third, sir, the tension on both sides will be the same, my brother? Are you getting it? Okay. "Sir, if this was moving?" I said, "If it was moving, then also the same answer would come." He said, "How?" I said, "Brother, suppose this is the pulley." "This is the pulley." "A mass is hanging here, and another mass is hanging here." "And suppose it is going upwards with acceleration a." "So, later we will see this thing that brother, is this clear to you?" He said, "Suppose the tension here is t." "The tension here is also t." I said, "Okay, brother." "So, here the tension will be 2t." I said, "Okay, brother." Okay. "Let's put the mass of the pulley * g downwards for a moment." I said, "Okay." "So, you will write the equation like this, won't you?" "Sir, if I write the equation for just this part, then you will write the equation." "Sir, how much force is acting upwards?" "2t." "Which force is acting downwards, sir?" "t + t + mg. This downward force is acting." I said, "Okay, brother. You are absolutely right." "So, upward force minus downward force equals sir, mass of the pulley * acceleration." He said, "Yes, sir, you are absolutely right." "So, for now, I don't know what 2t will be." "So, for now, I'll do one thing." "Let me call this t3 for a moment." "This t, this t, so this t3." "So, you will write here, sir, upward force minus downward force equals mass * acceleration." I said, "Okay." "Now, you tell me, what kind of pulley is this?" "Ideal." "What is the mass of an ideal pulley?" "Zero." "This means you will put its term as what?" "What will you put its value as?" "Zero." "And you will also put its value as what?" "Zero." As soon as you put this value as zero, then look carefully, what will T3 be equal to? "It will be 2t." So, in short, I want to say that whether the pulley is moving upwards, or your pulley is at equilibrium, or you have fixed it here like this. You just try to catch one pattern here: t, 2t. In a similar manner, suppose the diagram is given in this type of way. He said, "Brother, the rope is tied in this way." So, try to catch this pattern: if the tension here is t, or the tension in this rope is t, then what will be the tension in this, my brother? "It will be 2t." Are you getting it? "Upward tension equals downward tension." You have to do that. For any pulley, listen to me. For any ideal pulley, if any child is getting confused between t and t, then you do one thing. You just remember two points. What? "Sir, in such problems, if the rope is the same, then the tension is the same." First point is done. Second point, "Sir, the net upward tension equals the downward tension." For example, how much is acting downwards? T and T. For what? For this pulley. For what, my brother? For the pulley. He said, "Okay, sir." "For the pulley, you say directly." "Upward tension equals downward tension." "How much tension is upwards?" 2t. "And how much tension is downwards?" 2t. "So, it means upward equals downward." In a similar manner. "How much tension is here?" Upwards 2t, and downwards 2t. Are you getting it? Now, three types of questions are asked on this. Okay? The first question is about equilibrium, that your blocks, etc., the blocks are hanging, and they are in equilibrium. Okay? So, brother, tell me the value of the unknown block and the tension. This is the first question. In the second profile, questions are about constraint motion, that brother, this block is going with this much acceleration, this one with this much, so how much will this one go? Okay? And the third question is, brother, we have given the masses, etc., we have said that these masses are hanging. So, tell me, what will be the acceleration of which block? So, in pulleys, these three questions are generally seen. Now, we are discussing all of them one by one. First, I will talk about equilibrium questions. Equilibrium questions are very easy, my brother. Very easy. You just have to do one thing. What do you have to do, sir? You just have to try to understand one pattern: t, 2t, 2t, 2t, 4t. For example, I'll pick up questions from the problems. Understand carefully. For example, he said, "Find m if all masses are in equilibrium." I said, "Okay, brother." "Tell me the value of this mass." "If the mass is in equilibrium." To do such problems, do one thing. Assume tension t somewhere. Suppose the tension in this rope is t. So, look, this rope is the same. This t, so what will be the tension here? 2t. This 2t, 2t, 2t, 2t, so what will be the tension here? 2t. Try to catch this pattern: that the tension in this rope is t. So, t, he said, "Okay." This t, this t, so this is 2t. Are you getting it? I said, "Okay, brother." "Now tell me, is this in equilibrium?" "Is this mass in equilibrium?" "Yes, sir." "How much force is acting downwards?" mg. "What is the value of mg?" 100. "So, what will I write?" "Sir, upward force equals downward force." Okay, sir. "Sir, this one is also in equilibrium, isn't it?" He said, "All masses are in equilibrium." "So, mg will also be acting downwards on this." "So, upward force equals downward force." So, you will say directly, 2t will be equal to mg. Put the value here, so 200 will be equal to m * 10. What will be the value of mass? 20 kg. This is a very basic fundamental question. First, clarify the basic fundamentals. Then we will gradually level up. Like, let's see other questions, like this question. He said, "Brother, tell me the values of m1 and m2." So, I have put a screenshot of the book here. I have also written the SKAC point here: the way to do such problems is to assume tension t in any rope, in any rope, at any place. But try to assume tension such that after t, you get 2t, after 2t, you get 4t. For example, in the problem, if I assume tension here, this will come to you gradually. Okay? If you do four or five questions, you will understand on your own. Okay? Suppose I assume tension here. "So, what is acting downwards, sir?" "mg is acting downwards." "So, okay." "Take t here." "So, look, this t, this t, so what will be the tension here?" 2t. "Sir, 2t, 2t, 2t, 2t, 2t, 2t, 2t, 2t." "So, what will be the tension here?" 2t. "Sir, okay." "Sir, this 2t, this 2t, the tension in this rope is 2t. Here also 2t, so what will this be?" 4t. 2t, 2t, 4t. Okay. 4t, 4t, 4t, 4t. "So, what will this be, my brother?" 4t. I said, "Okay, brother. Let's move forward." "Sir, now tell me, sir, it is in equilibrium." I said, "It is in equilibrium." "He said, yes, guru ji." "So, what will t be equal to?" 100. "This is also in equilibrium." I said, "Absolutely right." "So, what will 2t be equal to?" m1 * g. "Sir, this is also in equilibrium." "How much force is acting upwards?" 4t. "And how much force will be acting downwards, my brother?" m2 * g. "So, you will say directly, m2 * g." "Now, put the value of t here." As soon as you put 100, m1 will come out to be 20 kg. As soon as you put this 100, m2 will come out to be 40 kg. This will come. You will get these values of m1 and m2. Are you getting it? Clear? Let's see more questions. I have put many questions. Try here if possible. On the rough copy, quickly, on the rough copy, try all the children quickly, before a minute. Okay, okay, sir. Let's move forward. Sir, how will it be done? I said, "Look, suppose the tension in the rope is t." Okay, sir. "What is acting downwards, sir?" "mg is acting downwards." So, okay. "Take t here." "So, look, t, so the tension here will also be t." "t." "So, the tension here will be 2t." I said, "Okay, brother." "Now, look at this rope. The tension in this rope is t. The tension in this rope is t. So, what will be the tension here?" "It will be 2t." I said, "Okay, brother." "Come, let's solve it." He said, "Sir, it is in equilibrium." "So, upward force equals downward force." I said, "Okay, brother." "So, this upward force equals this downward force." And t will come out to be equal to m2g. "So, from here, it is clearly visible that the value of m2 is how much?" He said, "m2 is 10 kg." "It has come." m2 is 10 kg. Your answer is 10 kg. Next, let's move forward. Let's talk about this. "Sir, 2t is acting upwards, and m1g is acting downwards." "So, you will say directly." "2t will be equal to m1 * g." "So, what will be the value of m1 here, brother?" "It will come out to be 20 kg." Say. Are you understanding? Hold on for 1 minute. Yes, brother. Okay. "So, suppose I have placed this problem on an inclined plane." "Such problems will also be formed." "That I have placed it on an inclined plane." "So, first I will do four or five questions." "Then I will give you questions to do here." "Suppose this question is given, brother." "The whole setup is here, and I write here." "All masses are in equilibrium." "All masses are in equilibrium." "If I don't write it in any question, then understand that it is the case where all masses are in equilibrium." Okay, sir. "So, sir, all masses are in equilibrium." "So, the net force on all of them should be zero." "Draw its FBD." "On that." "Upwards, tension will be acting upwards." "Downwards, mg will be acting." "The value of mg will be 100." "Sir, t, t, so here it will be 2t." "Sir, this 2t, this 2t, so this will be 4t." "And what will this be here, my brother?" 4t. Okay, sir. "Sir, it is in equilibrium." "So, t will be equal to 100." I said, "Okay, brother." Okay. "And this is in equilibrium." "So, how much force will be acting here?" "mg sin theta." "So, you will say directly that 4t will be equal to mg sin theta." "Here, quietly put the value." "What is the tension, brother?" "The tension is 100." "Is the sound coming?" "Is the sound coming?" "Coming, coming." Okay? "The tension is 100." "So, brother, put the value." "4 * 100 will be equal to m * 10 * 1/2." "Solve it calmly, brother." "10 cancels out 10." "What will m be equal to?" "It will be 80 kg." "Your mass will come out here." Okay? Next, let's move forward. Let's look at one more question. Suppose it is of this type. Sometimes it also happens that a block is connected to two or eight ropes. "So, do not make a mistake there." "Suppose the tension in the rope is t." "So, look, t, so the tension here will also be t." "t." "So, the tension here will also be t." "t." "So, it means if you draw the FBD of this mass, then t will be acting upwards." "This t, this t, so what will be acting upwards here?" 2t. Okay. Okay, sir. Okay. "So, sir, if it is in equilibrium, brother." "So, what will this be equal to?" "Sir, t = mg." "Okay." "All masses are in equilibrium." "If you talk about this, then 2t and t, it becomes 3t." "It has become 3t upwards." I said, "Okay, brother." "So, it has become 3t upwards." "And 3t, my brother, is equal to what?" "Sir, the total upward force is 3t, which is equal to 300." As soon as you solve it, it means if you take the ratio, then three will be equal to. I think t is coming out to be 100. "So, the mass will be 10 kg." Okay? Okay, sir. 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It is equal to 100. So, as soon as you put the value here, it will come out. Your answer for m will come out to be 60 kg. Your answer will come out. Next, similarly, a question of this appearance might be given, brother. No problem, brother. This entire system is in equilibrium. He said, tell me, what will be the mass of the lower platform, m? He said, brother, the entire system is in equilibrium. So tell me, brother, what will be the mass of the lower system, the lower platform? I said, brother, look, assume its free body diagram. Tension will be acting upwards, mg 100 will be acting downwards. So this block is in equilibrium. So t will come out to be equal. I said, okay, brother. Let's start. After this, he said, sir, look, sir. T is also in this. So this is 2t, sir. This 2t, look carefully. This 2t, 2t, 2t, 2t, 2t. So the tension in this rope is also 2t. This 2t, this 2t. So this is 40, 4t, 40, 40, 40, 40, 40, 40, 40, 40. Okay. So you will say from here, 4t, 2t, 60, and t, 70, 70. Look carefully. How much mass is above it? 4T, 2t, 60. And this is t, 70. Okay? 70 is equal to what, sir? 70 is equal to, my brother. It is equal to m * g. I said, okay, brother. And what is the value of t, brother? 100. This means the mass will come out to be 70 kg. Okay? So try to understand this pattern. After this, this question is very easy. Now I am giving you some questions here for homework. And I will give some questions for now. So, all the children, look carefully here. Okay? I have put some questions here. You try these questions. This is a question, and its solution is in front of it. This is a question, and its solution is in front of it. This is a question. Its solution is in front of it. This is a question. All of these, well, I have already done this question. Sorry. This is a question, and its solution is in front of it. You can try it yourself. Question, its solution in front of it. Question, its solution in front of it. Okay? Question, its solution in front of it. This question, this question, well, we have already done this. Okay? We have already done this question. Okay? So I will delete this. Okay? So this is the question, my brother. I have put the solutions in front of it. You can try these questions peacefully. By the way, let me tell you, okay? This book, SKC, is available on Flipkart and Amazon. Okay? Okay? Okay? In this, I have taken each chapter in a good way. This is the entire 11th class part. In this, the entire thing is in a good way. The notes are in a fantastic way, properly synchronized, in a proper sequence, from basic to advanced level. Okay? You will find good questions in this, and you will also find basic concepts. You will find it in SKC. Many, you know, I will condense things paragraph by paragraph into two or three lines, with memes also. I have written it in an entertaining way. You will find all the notes in this. You will also find good level questions. It is also available on Amazon. It is also available on Flipkart. Okay? It is a bestseller on Amazon. Okay? If any student wants to buy it, they can definitely buy it. But if you feel that sir, I cannot buy it, then it's okay, beta. Don't think that sir, you are promoting so that we buy it. Okay? You will benefit from buying it. And if you feel that you cannot buy it, then it's okay. Join the Telegram channel. I have uploaded the PDF of its chapters there. Okay? So you can read from the PDF there, or you can get a Xerox of that PDF and read from there. Because, obviously, the real fun doesn't come from reading from a PDF. The real fun is from a hard copy. Okay? So I have uploaded the PDF in the Telegram group. I keep uploading PDFs chapter-wise there. You can download it from there and read it properly. But I would say, please try to solve all the questions if possible. I have condensed the entire theory in simple language. Okay? Let's move on. Now let's do one more thing. I will show you some questions. You have to pause the screen now and try those questions. Okay? Your time starts now. Okay? I am just showing you a lot of questions. Okay? You have to pause the screen now. First, I will give all the questions and you try all the questions. These two questions. This question, this question, this question. Okay? For now, I am giving you this many questions. 1, 2, 3, 4, 5, 6. All six questions should be absolutely correct. Pause the screen and try. Let's start. Okay, sir. Come, let's start. Sir, look, sir. Let's assume the tension here is t. This t, so this will also be t. I said, okay. t, so this will be 2t. This 2t, so this will also be 2t. Sir, it is in equilibrium. t will come out to be 100. I said, okay, sir. It is in equilibrium. t will come out to be m1g. Sir, it is in equilibrium. 2t will come out to be m2 * g. As soon as you solve it, m1 will come out to be 10 kg, and m2 will come out to be 20 kg. Okay? Next, sir. Its mass is suppose t. This t, so how much will this be? 2t. How much will this be? t. This t, this t, so this will be 2t. t is equal to 100. So from here, we will write t is equal to 100. I said, okay, brother. So 3t will be equal to m * g. So, brother, solve it here. Put the value of t. So m will come out to be 30 kg. Please solve this. Sometimes we get the answer three times. Sometimes the diagram is made in such a way that we get three times less. That's why I will say, don't use any shortcuts. Do it peacefully, calmly, because getting such a question wrong is a big sin. Okay? Such questions should not be wrong. Next, similarly, he said, okay, sir. Assume the tension here is t. Look at t, how to look. Rope is the same, so tension is the same. t, here also t, here also t, here also t, here also t, here also t. So this is t. This t, this t, so this is 2t. This t, this t, so this is 2t. Now t is equal to 100. So this means m1g. Now I will write directly here, m1g. If you solve it, then sir, t is equal to 100. So 2t will be equal to m1g. So m1 will be equal to 20 kg. And this means m2 will come out to be 30 kg. Okay? Next, I move forward. Next question. Suppose it is given like this. I think we have already done this question. So let's remove it for now. Let's solve it anyway. This tension, t. Below it will be acting, c, tt, it will be acting, tt, 2t. So this will come out to be 2t. Sir, 2t will be equal to mg sin theta. Sir, what is the value of t? The value of t is 100. Put 100 here. As soon as you put 100, it becomes 200. So m will come out to be, my brother, 40 kg. Okay? It is possible that they put inclined on both sides. No problem, brother. Put inclined on both sides. Assume tension t in this. t, this also t, this also t, this also t. Why? This rope is the same. Look, t, this tt, t. So this will be 2t. Next, next part. Sir, make its free body diagram. t will come out to be equal to? The one on the right, 4mg sin theta. mg sin theta will be how much? 100 sin 30. 100 sin 30. mg sin theta. 100 sin 30 will be how much, brother? It will be 50. Put the value of t as 50. If you put 50, it becomes 100 above. So m1 will come out to be 10 kg. Talk about this. The tension on the right will be equal to m2g sin 37. So solve it peacefully. You need to find the value of tension here. Sir, the value of tension is 50 = m2 * in. Sir, g sin 37 is six. sin 37 is six. So m2 will come out to be 50 / 6. Okay, brother. Next, next question. Just like this, you will not see such questions. But still, to remove your fear, I have given the question. If you do this, it means you will practice all the questions. I have asked here. Tell us the value of m1 + m2 + m3 / m4 + m5 + m6. You will directly say, sir, assume the tension in this rope is t. So look, t, here also tension t, here also tension t. Take this t. Okay? This t, this t, so this is 2t. I said, okay. This t, this t, so this is 2t. 2t, 2t, 2t, 2t, 2t, 2t, 2t, 2t. So this will be 4t. 2t, 2t, 2t, 2t, 2t, 2t, 2t, 2t. So this will be 2t. This is 2t, this is 2t, this is 2t, this is 2t. So this is 40, 40, 40, 40. This will also be 40. 40, 40, 40, 40, 40. So this will also be 40. This is 40, this is 40, so this will be 80. Look, catch it like this. Force above = Force below. For the pulley, 2, 40, 40, what is 80? So 80 tension will come below. This is 40, so this is 40. Rope is the same, so tension is the same. If this is 40, then in this rope, tension will be 2t, and in this rope, tension will be 2t. Don't make it 80, 80 here. Okay? Mistakes happen here. Let's start the question now, brother. First, find the value of t, brother. What do we understand from the value of t here? Sir, it is in equilibrium. I will write it here. All are in equilibrium. This is very important to write. Okay, sir. So 3t = 300. 3t = 300. So t comes out to be 100. If t, then I will write the answer directly. Look, okay, sir. Sir, tell me, what will m1 be? m1 will be t = m1g. So this means m1 is 10 kg. Plus, sir, what is t? It is 100. So this becomes 400. If it is 400 above, then 400 force should act below. So what should m2 be? 40. Plus, sir, tell me about m3. What is t, my brother? T is 100. So it becomes 200 above. So to have 200 below, what should m3 be? It should be 20 kg. Okay? Let's move forward. Okay. Tell me m4. Sir, how much is above? Sir, it is 800. So how much is below? 80. Next, let's move forward. It is above, sir, 20, meaning 200. So below it will be m4. m5 will be 20. Sir, tell me here. Sir, above is 2t, 2t, 2t. If it is 2t above, then below, meaning above is 200, then below it should be 20. As soon as you solve this, 40, 50, 70, 70 / 120, 7 / 12. The answer is going. I hope I am not making any mistake. 4, 2, 6, and 1, 7, 8, 2, 10, 2, 12. And if all these questions are correct for you, and if you enjoyed the equilibrium questions, then pause the screen now and type in the comment box below: Yes sir, we will nail the equilibrium questions. We have understood them well. Now let's move to the next part. If anyone wants to note these questions, my brother, then note them down. Okay, brother. Now let's move to our most important part, which is the application of f = ma. Meaning f net = mass * acceleration. On which we will learn to apply Newton's laws of motion to any block. Basically, many forces will be acting on it, and it will have acceleration. Basically, we are now moving out of equilibrium questions. In equilibrium questions, the net force was zero. The force in front was greater than the force behind. The force above was equal to the force below. Now we are talking about, suppose, on a block, for example, if I tell you, this is some block. I applied a force F1 in front, and a force F2 behind, my brother. I said, okay, child. A force F1 is acting in front, and a force F2 is acting behind, my brother. He said, okay, sir. And due to this, suppose its acceleration is A in the forward direction. I am writing this that F1 is greater than F2. So for any block, even though I am talking about two forces now, there might be three forces or four forces. You learn this: first, sir, in which direction is the acceleration of this block? Forward. In which direction is the acceleration of this block? Forward. This means the force in front will be greater. In which direction is its acceleration? Forward. This means the net force on it will be in the forward direction. Wherever the net force is, the acceleration of the particle will be in that direction. So I can write, sir, in this case, sir, the force in front minus the force behind equals mass * acceleration. What have I written as f1 - f2, my brother? I said, I have written this as f. Clear? Similarly, suppose you have a question in front of you, a mass m is falling in this way. So mg is acting downwards on it. Tension is acting upwards on it. And suppose its acceleration is a upwards. So you should be able to write this equation: if its acceleration is upwards, then the upward force is greater. This means we will write upward force minus downward force, this is the net force. Net force equals what, sir? Mass * acceleration. Are you understanding? And if suppose in a question, in a question, a situation like this comes in front of you, then you will say, sir, if the acceleration is downwards, a, then you will say, downward force minus upward force equals mass * acceleration. Are you understanding? For this, let's first understand with a question. For example, I have taken the first question. I said, brother, this is a 20 kg block. Okay, brother. Let me make another copy of this. Sir, sir, these are two, sorry, not 20 kg, but two blocks of 2 kg and 3 kg are placed. And we applied a force of 20 Newtons in front. The question will ask, what is the acceleration? What is the common normal between them? It will ask these two types of questions. Either it will ask for the normal, or it will ask for the acceleration. If you want to solve it properly, properly, then you will say, sir, let's look at one question properly. Sir, make the free body diagram of the 2 kg person. Sir, mg is acting downwards, normal is acting upwards, they cancel out. Sir, a force is acting in front, f = 20 Newtons. Sir, a normal reaction will be acting behind. Sir, its acceleration will be in the forward direction, a. So we will write, force in front minus force behind equals mass * acceleration. Sir, why is the normal acting behind? Brother, it is touching it. Normal is always towards the body. I said, okay, let's go. He said, now if I make the free body diagram of 3 kg here, I have made the free body diagram of 2 kg. If I, my brother, apply a force to 3 kg, then I will write, sir, how much force is acting in front? I said, brother, normal reaction is acting in front, due to which its acceleration is A in the forward direction. Normal is acting in front, due to which its acceleration is A in the forward direction. He said, okay, sir. So I will directly write, sir, n will come out to be 3 * a. Why? Because only one force is acting in front, man. f = ma. Okay. If I solve both of them. If I put the value of n here, I put the value of n here. So 20 - 3a = 2a. So a will come out to be 20 / 20 / 4, sorry, 20 / 5. So your acceleration will come out to be 4. And as soon as you put the value of acceleration here, the normal will come out to be 12. So this is the fundamental method. Remember this one line: whenever someone asks you for normal and tension, you will make the free body diagram. Whenever someone asks for normal and tension, you will make the free body diagram. This should be the first step. I said, okay. Now, as this looks like a lengthy method, but we should know it. We should know how to make individual free body diagrams. But now let's see how to do such questions directly. As soon as you see it, you will say, sir, look. I said, yes, sir. Its acceleration will be A, so its acceleration will also be A. I said, okay, sir. Let's consider both as a system. I said, okay. So I am writing directly, F net = total mass * acceleration. Sir, what is F net? Sir, it is 20 Newtons. Meaning, understand it this way, I have assumed both of them as one block. I have assumed both of them as one block. He said, okay, sir. Assumed as a block. So, sir, how much force is acting in front? 20. What is the total mass, my brother? Sir, the total mass is 2 + 3, multiplied by its acceleration a. So what will be the value of acceleration? What will be the value of acceleration? 4. So you can write this directly from here. Where is the question? Directly. Just like we were writing before. Here we were going individually. From here, you can write directly. He said, so tell me, sir. Sir, tell me, how to find the normal? Brother, make the free body diagram. Brother. Make the free body diagram of the 3 kg block. As soon as you make the free body diagram of the 3 kg block. Normal will be acting in front, my brother. Due to which the acceleration is a in the forward direction. So n will be equal to 3 * a. 3 * acceleration value is 4. So normal will be 4 * 3 = 12. Understood? Okay, sir. Sir, here, here, suppose it is asked. I said, look, assume their acceleration is A individually in the forward direction. Okay, sir. So make its free body diagram. Not free body diagram. Now do it without free body diagram. Sir, how much force is acting in front? 50. How much is acting behind? 20. What is the net? 30. Write directly, sir. Force in front minus force behind equals total mass, which is 10 kg, multiplied by acceleration. Acceleration will come out to be 3. If he asks, tell me the normal between the 3 kg and 2 kg blocks. The normal between these two. So make the free body diagram of the 3 kg block. How much force is acting in front? f = 50. How much is acting behind? f = normal. Let's assume it is n1. Suppose the normal contact force between 3 kg and 2 kg is n1. So if you make the free body diagram of 3 kg, you will show the normal towards the back. Normal is towards the body. In which direction is its acceleration, my brother? Sir, its acceleration is in the forward direction, a. You will directly say, force in front minus force behind equals mass * acceleration. Put the value of acceleration as 3 here. So 50 - n1 = 3 * 3. So n1 will come out to be 41. If someone asks you, sir, sir, tell me the free body diagram between 2 kg and 5 kg. The normal between 2 kg and 5 kg. So you can either make the free body diagram of 2 kg or 5 kg. Let's say you make it for 5 kg. Okay, sir. Let's make it for 5 kg. So tell me, sir, make the free body diagram of 5 kg. How much force is acting behind? 20, sir. Sir, the 2 kg block will be applying force on it, normal N2 in the forward direction, due to which its acceleration is a in the forward direction. So what equation should I write, brother? Sir, force in front minus force behind equals mass * acceleration. And what is the value of acceleration? Sir? The value of acceleration is 3. n2 will come out to be 15 + 20 = 35. Understood? Okay. Okay, sir. For example, now the same question will be given for the rope. You apply the same thing for the rope. If I ask you, let's tell me, what will be the acceleration in this? Sir, assume its acceleration is in the forward direction, a. Its acceleration is in the forward direction, a. So what do you do? Consider this entire thing as a system. You will directly say, sir, if we consider the entire thing as a system. So what is the external force acting? He said, 50 is acting. Sir, f net = total mass * acceleration. Acceleration will come out to be 10. If someone asks, sir, tell me the tension. Make the free body diagram of the 2 kg block. Tension is acting in front on the 2 kg block. Due to which there is also acceleration in front. t = you will write 2 * a = 2 * 10 = 20. Done. Understood? Okay? Similarly, you can do this. Okay? Sir, make its free body diagram. Free body diagram? Consider the system of all three. 3, 2, 5, 10. How much force is acting in front? 50. So what will be the acceleration? 5. Acceleration is 5. Okay, sir. So this means, make its free body diagram. Tension t1 will be acting in front. So how much will t1 be? Sir, this tension itself is giving it acceleration. What is its acceleration? He said, 5 * acceleration was 5 * 5 = 25. And so on. You can make the free body diagram of any individual and there you can find the tension. If someone asks you, brother, tell me how much tension is in this rope. Then make the free body diagram of the 3 kg block. Tension t2 will be acting behind. So say, how much force is acting in front? 50. Tension behind t2 = mass * acceleration. Done. It is possible that they apply force in front and behind. Brother, in this case, tell me what will be the acceleration. So look, look carefully. Sir, f net = how much? Sir, total mass in such questions * acceleration. So acceleration will be f net / total mass. I said, okay. So I said, just try to catch this pattern and try to apply this pattern. If I ask you, tell me the acceleration, you will directly say, force in front minus force behind divided by total mass. 5 + 2 + 3. End of story. After this, you can make the free body diagram of any person and find the tension. And you can use the same pattern in the pulley system. For example, if I tell you, brother, we have taken a pulley system here. And I said, brother, its mass is 3 kg. And I said, my brother, here is a block of 2 kg. Take this. Okay, sir. Okay? This is the ground. I have released it. This is the ground. So this means, now if I ask you, I said, tell me, brother, how to solve the question? You will say, sir, solve it calmly, peacefully. We can write here. He said, what? I said, sir, if you make its free body diagram, then sir, assume it is going down with acceleration a. Then this will go up with acceleration a. Sir, mg30 will be acting downwards. Here mg20 will be acting downwards. Tension will be acting upwards. Here tension t will be acting upwards. Okay, sir. Okay? So now if I ask you, I said, tell me, sir. Tension is upwards. Tension is also upwards here. Sir, its acceleration is downwards, so its acceleration is upwards. What equation will you write for this? Sir, force below minus force above equals mass * acceleration. What will you write for this, sir? Sir, force above minus force below equals mass * acceleration. Sir, this cancels out. Sir, 30 minus 20 is 10. 10 = 5 * a. a comes out to be 2. This is the acceleration. Are you understanding? Okay, sir. Acceleration is a. Okay, sir. Acceleration is a. And sir, if t is asked, then I said, put the value. Put the value in this. What will you write? Sir, put the value of a here. 30 - t = 3 * a. Solve it. t comes out to be 24 Newtons. So this is done. You are solving the question peacefully. Solving by making individual free body diagrams. Now, there is another method for this. Shortcut method. What? He said, sir, tell me. Sir, mg is acting on this downwards, 30 Newtons. I said, yes, brother. Sir, mg is acting on this downwards, 20 Newtons. Yes, sir. The mg acting on this is trying to pull it down. It wants to pull me down, no matter what. Oh, it wants to pull it down. It wants to take it down. Meaning, this is your pulling force, and you can tell with this feeling that this 20 Newtons is trying to stop it. Are you getting it? 20 Newtons is trying to stop it. Meaning, if this were 3 kg, if this were 3 kg, then 30 here and 30 here, it would be in equilibrium. If this 30 wanted to pull, the other 30 would stop it. Sir, this 30 wants to pull. This one is weak. It is trying to stop, but it won't be able to stop. This means its acceleration will be downwards. So its acceleration will be upwards, a. So you catch this thing directly. What? He said, acceleration = pulling force - stopping force / total mass. Done. Understood? Okay? Now, for example, look at the question. Look at the first question. He said, sir, assume its mass is 4 kg. Assume a 6 kg mass is hung here. Okay, sir. He wants to say, sir, tell me, what will be its acceleration downwards? a. You will directly say, sir, acceleration = pulling force - stopping force. Sir, mg will be acting downwards, 60, which will be trying to pull it. I said, you are absolutely right, brother. Look, mg is acting downwards, 60. And here, no, here, here, mg will be acting, 40. Sir, the pulling force is 60, the stopping force is 40. Divided by total mass, sir, 4 + 6. It comes out to be 2. Done. If you are asked, brother, tell me the tension here. Make its free body diagram, brother. I am doing one question, after that you do it yourself. Sir, make its free body diagram. You will directly write, sir, force below - force above = mass * acceleration. Done. Done with the question. Say, this was just one question. More questions. Next question. I will do one thing. I will place masses on both sides. One mass here, here, one mass here, and one mass here. I said, its mass is 2 kg. Its mass is 5 kg. I said its mass is 3 kg. He said, now tell me, what will be its acceleration? I said, brother, assume its acceleration is downwards, a. Its acceleration will also be downwards, a. Its acceleration will be upwards, a. Acceleration = Sir, how many masses are here? Sir, 7 kg. So the total pulling mg will be 70. Sir, what is the stopping force here? 30. mg, how much mg is acting here? 30. Divided by total mass, which is 10. x comes out to be 4. Next question. Next question. He said, sir, suppose a question is given like this. Here a block is placed, and here a pulley is hung, and here an m mass block is hung. Assume it is 10 kg. And its mass is also, my brother, 10 kg. If I ask you, tell me the acceleration. You will directly say, sir, this will go, sir, downwards. Its acceleration will be a here, so its acceleration will also be a here. Sir, mg is acting downwards. The value of mg is 100. So the acceleration will be, sir, pulling force, stopping force, there is none. Minus stopping force divided by total mass, 10 + 10. This acceleration will come out to be 5. Now, don't do this, subtract mg mg here. Brother, mg is cancelled out by normal. Is there any force acting behind? No. So solve the question individually. Are you understanding? For example, see more questions on this. Sir, next question. Suppose I tell you here, I have hung a mass. This goes here.

It has been done. Here I have hung a mass. I have said this is a 3 kg mass. This is a 2 kg mass. Tell me whose acceleration will be in which direction? So what will you say? You will say, brother, let its acceleration be 'a' downwards. Then its acceleration will be 'a' upwards. Sir, acceleration equals sir mg, the pulling force is 30 Newtons, the resisting force is 20 Newtons, divided by the total mass 2 + 3 = 2. It can be done, so let's put one more in the middle here. So you say, brother, let's do it like this in the problem. 3 kg was here. We placed a block like this and brother, my friend, we hung a block here like this. You will say, sir, this is a 2 kg mass. This is suppose a 5 kg mass. This is suppose a 3 kg mass. They say, sir, now tell me what will happen? So suppose its acceleration is 'a' downwards. Then its acceleration will be 'a' upwards. Then its acceleration will be 'a' in this direction. Okay? If this goes down, this will go forward, and this will go up. So what will you write for acceleration? You will say, sir, we will write acceleration. Pulling force minus resisting force divided by total mass 2 + 5 + 3 = 1. How much will it come out to be, brother? One. Are you understanding? It is possible that they might place it on an inclined plane, brother. But if they place it on an inclined plane, it will be like this. They will say, brother, suppose this angle is 37°. Here we have placed a block of 10 kg, and here we have suppose hung a block of 20 kg. They say, now tell me what will happen? You will say directly, sir, this, this is heavier, so its acceleration will be 'a' in this direction. Its acceleration will be in this direction. So what will you write for acceleration, sir? How much is the pulling force, sir? 200. How much is the resisting force, sir? A force 'f' will be acting backwards on this, mg sin theta. Sir, mg sin 37. Sir, mg is 100. Sir, mg sin 37. 100 sin 37 will be how much? 60. You will directly write, sir, mg. Here the pulling force is 200. So the pulling force is 200, the resisting force is 60, divided by the total mass, which is 20. The problem is solved. Are you understanding? It is possible that they might place it on inclined planes on both sides. It is possible that this time they might place it like this, an inclined plane. They say, brother, this angle is 53°. Here a 10 kg block is placed, and here also suppose a 10 kg block is placed. And they will say, brother, the setup is made like this, and this angle is given as 37°. So what will you write, sir? Sir, mg sin theta will be acting on this in this direction. Sir, mg sin theta will be how much? 80. Sir, mg sin theta will be acting backwards on this. Sir, this will be equal to, sir, 60 because this is 37°. So, sir, if its acceleration is 'a' in this direction, then its acceleration will be 'a' upwards. So acceleration will be pulling force minus resisting force divided by total mass. The problem states this. Are you understanding? Pull as much as you can. Take more problems. Here is the next question. It is possible that this time they might give you a problem like this. Understand carefully. They say, brother, let's put a heavy mass here. Suppose a 10 kg mass is given here. And here I have hung, brother, a 2 kg mass. They say, now tell me, this angle is given as suppose 37°. So you will immediately say, sir, sir, its acceleration will be in this direction, its acceleration will be upwards. How did you know this, sir? How much is the pulling force, sir? mg sin 37, which is 60. How much is the resisting force? 20. How much is the total mass? 12. Problem solved. And if suppose, if suppose you are getting confused in such problems about where to assume the acceleration, then assume it wherever you want. If you are confused whether to assume it this way or that way, assume it wherever you want. Okay? If the acceleration comes out negative, then understand that you have assumed the directions incorrectly. Are you understanding? You have assumed the directions incorrectly. Okay? Okay, sir. Now let's look at an HCB question in this same problem. Now in the HCB question, a problem like this will be given. Here they will say, brother, suppose I have hung a mass here, 10 kg. I said, okay, brother. Sir, here we have taken a mass, suppose 10 kg. Okay? I am just taking random data here. And here I have taken a mass of 20 kg. They say, tell me what will be its acceleration? If this angle is 37°. So if you are understanding things, its acceleration will be 'a' downwards. This is 20 kg. It will push. This is 10 kg. It is light. Okay? So this means its acceleration will be 'a' downwards. So its acceleration will also be 'a' in this direction. Its acceleration will also be 'a' upwards. So what will I write for acceleration? Look carefully. Sir, how much is the pulling force here? Sir, the pulling force is 200. Sir, its mg sin theta will also be coming here. I said, okay. And here the resisting force is, brother, 100. Divided by the total mass, how much will it be? 20 + 10 + 10. What will be asked here? Tell me the tension. t - 100 = 10 * a. The value of a. So you will find it from here. These are your HCB problems. Are you understanding? I will show you the questions now. Meaning, now I have full confidence. No matter how many are put. Okay? Look at this question, brother. Look at a triple S Q problem, brother. Salim Sir Special Question. Triple S Q Salim Sir Special Question. They say what? I said, brother, now you will apply it vigorously. Oh, vigorously. Put one here. Put one here. Okay. Put one here. Okay? Put one here. In this way, we see such problems in class. Okay? Now you will do it. They say, brother, suppose this angle, I say, suppose it is 30°. This is 37°. Sorry. Suppose its mass is 20 kg. I said, okay, brother, 20 kg is its mass. Its mass is 10 kg. Its mass is 10 kg. Suppose its mass is 10 kg. Write its mass, brother, 5 kg. 5 kg. I said, okay, brother. Suppose this angle is 30°, and let's make this 37°. They say, tell me what will be the acceleration? So you have to see which force is supporting and which force is resisting. Okay? Now 'a'. Sir, if we talk about this, it is 20 kg, so its mg will be supporting it, meaning its acceleration is 'a' downwards, so its acceleration will be 'a' in this direction, its acceleration will be 'a' in this direction, its acceleration will be 'a' in this direction, its acceleration will be 'a' in this direction. So what will you write for acceleration from here? Pulling force 200 plus here mg sin 37 plus nothing is happening here. Normal mg has cancelled out. Its mg sin 30. mg sin 30 will be 50. It is trying to resist. Its mg sin theta is trying to resist it. And its mg sin theta is also trying to resist it. Its mg is also trying to resist. It is 5 kg, so mg will be acting downwards, equal to 50. Okay? It is trying to resist. Its mg sin theta is also trying to pull it down. So look at what is opposite to the acceleration. Put those with minus. Sir, all forces have come. 1, 2, 3, 4. All forces have come. Divided by total mass. How much is the total mass, brother? 5 + 10 + 10 + 10 + 20. Whatever the answer comes out after solving, your acceleration will be calculated. I think now you will do these problems with a smile. Now you look. You look at the HCB problems. Look at question number one. I think you will do it as soon as you see it. HCB. This is your homework. Next, the next part. Look at this next question. This says, brother, the value of f is m2g / 2. So tell me the acceleration. So look, how much force is acting downwards? m2g. So look, what will I write for acceleration? Sir, sir, m2g is acting, and we have applied an extra force, m2g / 2, meaning half of it. So its acceleration will be in this direction, 'a'. So what will you write for acceleration? Sir, pulling force minus resisting force divided by total mass m1 + m2. Solve it. After this, solve the problem. Look and see, these are HCB problems. Look at this, this, this 5, 3. So this will be 53°. This will be 37°. Now say, sir, how did you write this? This is a length of five. The angle between a length of 3 meters is called 53°. After this, sir, what will come here? Sir, m2g. You will write 'm', right? After this, acceleration. How much is the pulling force, sir? Its mass * g * sin 37. How much is the resisting force? Its mass * g. Okay. Okay. This angle is larger. This means it will move in this direction. Its acceleration will be in this direction, and its acceleration will be in this direction. This is correct. So what will you write for acceleration, sir? Acceleration will be written as, sir, how much is its pulling force? mg. How much is it? 10 sin 53. Resisting force is 10 sin 37. mg sin theta will be resisting one, and supporting one. Divided by total mass. The problem is solved. It has come. Do it after this, whatever the answer comes out after solving. What is asked? Acceleration of two blocks. I will find it. Come on, since I have done this much, I will do this much too. Look, 10 will come out as common. 10 / 4. Sir. How much is sin 53? 5 / sorry, 4 / 5. How much is sin 37? 3 / 5. How much has this come out to be, sir? This has come out to be, sir, 1 / 5. Is it going 1/2? 1/2? Oh, one is going, brother. Where did the mistake happen? It is saying g / 10. g / 10 means one. One minute, I will check. Oh, sorry. Mass, I have mass, it will be 1 + 1, right? Mass will be 1 + 1. Okay? So how much will this come out to be? 10 / 2. This will come out to be 'a'. Okay? Next, let's move forward. Now look at this problem. I just told you, do this calmly at home. This is your homework. Okay? This is your homework. Try it calmly at home. And believe me, these are among the most difficult problems of HCB. Now, for example, this question says, HCB. An external force is applied to this. No problem, it has been applied, brother. Look, how much is m1? 5 kg. It said, my brother, this is a 5 kg block. Okay, sir. How much is m2? 2 kg. It says, brother, this is a 2 kg block. And how much is f? 1 Newton. This has also been applied an extra force of 1 Newton. And this also an extra force of 1 Newton. Okay? It said, tell me the acceleration. So what will we write for acceleration? Okay? What will you say? Sir, the pulling force, the heavier one, 5 kg. This means its acceleration is 'a' downwards, so the acceleration of all of them will be 'a' upwards. The one that is heavier will be pulled towards it. So tell me, how much is the pulling force of 5 kg? 50. Plus 1 Newton, you are pulling. Okay? Resisting force. This, this is supporting it. Sir, how much is the resisting force from here? 20. And sir, 1 Newton is also trying to resist it. But this total mass, how much is the total mass, brother? Sir, 2 and 5, 7. How much has it come out to be, brother? 30 / 7. 7 * 4 = 28. Remaining 2. 7 * 3 = 21. Story finished. Are you understanding? So in this way, you can do these questions. Just try to understand a pattern. Pulling force minus resisting force divided by total mass. Okay? Okay. If you want, type it in the comment box right now if you have understood all this. Say it right now, yes, brother, whenever such a problem comes, you will apply the ESC method here. They say what? Sir, Salim Bhaiya's favorite line: pulling force minus resisting force divided by total mass. Type this in the comment box below, and then we will move to the next article. Clear? Okay. Does anyone need to note anything, son? Note down all the old questions that I have solved just now. Okay. Now let's do one thing. Let's move to some problems that you often get to see in every exam. You get to see them in test papers. You have to face such questions in every book. So let's take a look at them once, where and in which questions we need to avoid which mistakes and how to deal with the questions. For example, I have written a question here in front of you. Here it is given, brother, a 10 kg block. A 10 kg block. There is a rope in the middle, which is massless. And he said like this, brother, we have applied a force upwards, sir, 600 Newtons. Then find the acceleration of each block and the tension at point A. Okay? Okay, sir. So, sir, how much will the acceleration be? Sir, look, 600 is acting upwards. The total mass is 20. So 600 / 20 = 30. Often, often, meaning 30 to 40% of students give this answer. And they will directly say, sir, look, how much will acceleration be, sir? Sir, 600 is acting upwards, and how much is the total mass? 10 and 10, how much is it, my brother? 20. So how much will it be, sir? 30. Which is actually wrong. Okay? Which is actually wrong. They say, why is it wrong, sir? Why are you saying that? I said, brother, I am saying that because if I draw its free body diagram here, then mg will also be acting downwards, won't it? mg will be acting downwards on this. mg will be acting downwards on this too. Sir, I didn't think of that. mg will be acting. I said, yes. Look, I will call it the correct problem only when I mention it like this. If I have given it like this, then it will be understood that brother, there is gravity below. But definitely keep this in mind. Sometimes, sometimes in some problems, it is not mentioned. In some problems, the information is not given. So, brother, in that case, you have to consider this thing, that if the diagram is made like this, then yes, brother, mg will also be acting here. Yes, if the language of the question is like this, that brother, there are two masses, 10 kg and 10 kg, and both are on a horizontal floor. Both are on a horizontal floor. If he has given it in such language, then there is no problem. Then your answer is correct. Then what you calculated, f / total mass, that is your answer. But if the diagram is made like this, then you have to consider this thing, that gravity is also acting downwards. So, sir, now tell me how to do the problem? I said, look, brother, the acceleration of both will be the same. Okay, sir. The acceleration of both will be the same. Sir, the acceleration of the upper one will be upwards. So, sir, its acceleration will also be upwards, so its acceleration will also be upwards. I said, exactly, it's the same connected problem as yours. So, can I do one thing, sir? If I consider both as a system, can I say that mg will be acting downwards, which is 200? Are you understanding? Okay, sir. So what will you write for acceleration? You will directly write, sir, acceleration equals sir, pulling force minus resisting force divided by total mass, which will come out to be 20. Clear? Now if you ask, sir, tell me the tension at A. What will be the tension at A? I said, tension at A, so draw the free body diagram of this much part. If you draw the free body diagram of this much part, then this is a 10 kg mass. Point A is here. You draw its free body diagram. Tension at A will be acting upwards, and you are seeing this entire system moving upwards with acceleration 'a'. What will you write? Upward force minus downward force equals mass * acceleration. Look, this rope is massless, no problem. A 10 kg mass is hanging below, so how much will be acting downwards, brother? 100. So upward force minus downward force equals mass * acceleration. The value of acceleration is 20. After solving, your 't' will come out to be 300. Are you understanding? Often, sometimes what happens is, this massless rope, it will give its mass. Like the next question. Okay? Now you do the next question. I have given this rope with mass. Now this is not a rope with mass. Now this is a rope with mass. Now this rope also has mass. Suppose its mass is 10 kg and its length is 10 meters. So tell me, how much will be the tension at the midpoint of this rope? And what will be the acceleration? Quickly pause the screen. Try it. Okay, sir. Okay. Sir, look. I said, yes. Sir, acceleration, now we will write directly, sir. Sir, acceleration will be, sir. Pulling force. How much force is pulling upwards? 600. Minus resisting force, sir, what will be acting? I said, 100, 100, and 100. Total 30. It has become 30 kg, so mg will be acting downwards, 300. Divided by total mass. How much will be the total mass? 10 + 10 + 10. 300 / 30 = 10. It has come. 10 meters per second upwards. Meters per second squared. Okay? If someone asks, sir, tell me the tension at point A, then will you draw the free body diagram of this much part? They say, yes, sir, that's absolutely correct. We will draw the free body diagram of this much part. This is, brother, like Thor's hammer. It's like Thor's hammer. You will say directly, sir, let's talk about here. This is point A. I said, okay, brother. And this will be, sir? This will be 10 kg. I said, let's move forward. Sir, what is its mass? I said, what is its mass? I said, its mass is 5 kg. Its mass is 10 kg. What will you write? Sir, upward force minus downward force. How much will be the downward force, sir? Sir, sir, if you draw the free body diagram of this much, then tension at A will be acting upwards. And downwards, how much will be acting, sir? 10 and 5, 15. So this means upward force minus downward force equals mass * acceleration. And how much is the value of acceleration? 10. So how much will tension at this come out to be, my brother? 300. Are you understanding? Clear? Okay, brother. Sir, we have taken this rope with mass. So in this, you also get to see a question where we have placed the rope with mass on a horizontal floor. Okay? And we have applied a force forward. I said, okay. Actually, I don't write, son. I have to write first here so that I can save some time. Okay? Otherwise, this lecture will become very long. Okay? That's why I have written the questions here so that you can read the questions if you want. What is in the problem? I will do the first problem. You do the next problem. Sir, here, there is a road. I said, okay, brother, this is a road. Okay? Call it a road or a rope with mass. Sir, its mass is 10 kg and its length is 10 meters. I applied a force of 100 Newtons forward. So what is needed? They said, sir, first of all, we need, sir, tell me the tension at point C. Okay? And tell us at any distance 'x' from any point 'a', brother, if we go to any general point, any general point, pick any point 'x', then how much will be the tension at that point? We need this. I have given two questions here. Suppose I have considered this as a general point P, at a distance 'x'. So tell me how much will be the tension at point P? I hope the question is understood. Let's see how to do such questions. They say, sir, you just understand it like this, sir, it's a block, it's a simple matter. Okay, let's assume it's a block. Sir, where is the tension asked? Tension is asked here. So, okay, sir, wherever the tension is asked, sir, draw the free body diagram of that much part. So if I draw the free body diagram of this much, then look carefully, all children. They say, sir, what is in this problem? I said, there is nothing in this problem. You are asking for tension at C, right? I said, yes. So just draw the free body diagram up to C, erase the rest. Okay? Okay, sir. If I draw its free body diagram at point C, look carefully. They say, sir, this is point C. So, sir, sir, draw its free body diagram. Sir, tension, and suppose tension is away from the body. Sir, tension will be acting forward. TC. I said, okay. Sir, you applied a force of 100 forward. This means this entire road must be going forward with an acceleration of suppose 'a' in this direction. I said, okay. So if I find the acceleration, then it means I can find the tension. How will I find the acceleration? You will say directly, sir, consider both as a system. How much is the action force, sir? 100. So acceleration will be, sir, pulling force. There is no resisting force. Divided by total mass 10. Acceleration comes out to be 10. This means, this means, its acceleration in this direction will be how much? Sir, its acceleration will be 10 in this direction. So now if I ask you, I said, brother, tell me the tension here. So draw the free body diagram of this much part. I said, okay. How much force is acting forward? They say, forward force is tension at C. Sir, no force is acting backwards. Equals mass * acceleration. They say, whose mass do we need? I said, brother, I need the mass of that much part for which you have drawn the free body diagram. So if C is the midpoint. I am writing midpoint here. Sir, what is the mass of this rope? 10 kg. So how much will be its mass? 5 kg. So what will be tension? Its mass * its acceleration equals 5 * 10 = 50. Are you understanding? Okay, sir. They say, no, we want it at a general point. I said, tell me at a general point. So let's find it at a general point. So what will we write, sir? They say, sir, look, the acceleration will also be this much here. I am writing it here. Find tension as a function of x. Sir, the acceleration will still be this much. Why? Sir, consider the whole as a system. mg is acting downwards. Normal is acting upwards. It has cancelled out. Which force is acting forward? 100. Is any force acting backwards? No. So how much will acceleration be, sir? Forward force minus backward force divided by mass 'm'. So how much will the value of acceleration be, brother? Sir, the value of acceleration will be 10 here. I said, okay, brother. How much will the value of acceleration be? Sir, the value of acceleration will be 10. I said, okay. Now I need tension at P. So no problem, man. If you need it at P, then draw the free body diagram of this much. Here you go. Draw the free body diagram of this much. I said, okay, brother. So can I write like this? If you draw its free body diagram, then tension will be acting forward. You will directly write tension equals mass of x * acceleration. Sir, why are you writing like this? I said, this force is giving acceleration to this much part of the rope. So f equals, I have applied ma. If you want, you can also treat it like a block. Some children treat it like this. They say, sir, suppose this is a block, and the rope, and this is another block. Meaning, this is a separate block, and the part of the rope ahead is a separate block. Some children solve it like this too. That answer is also correct. That method is also correct. You can apply it like this too. Okay, sir. Okay. So tell me, sir, now the problem came. Sir, what will be the mass of x? What will be the mass of this rope? So for this, there is a bit of unitary method. Here they say, sir, is the value of x given? 1 meter, 2 meters, 3 meters. But the new value is not given. So, sir, do one thing. I said, what? They say, apply the desi method. Sir, the mass of 10 meters of rope, sir, the mass of 10 meters of rope is 10 kg. I said, yes. So the mass of 1 meter of rope will be 1 kg. I said, yes, brother, you are absolutely correct. Unitary method. So what will be the mass of x meters of rope, x kg? I said, you are absolutely correct. The mass of x meters of rope will be x kg. So this means, sir, can we write here, sir, the mass of x? I said, it will be x kg. And how much is the acceleration, brother? 10. So what will be the tension, 't', that comes out? 10x. Sometimes, maybe the graph asks you. They say, tell us the graph of tension versus x. So you will directly say, sir, t = tan 10x. This will be the graph of y = mx, whose slope will be 10. Are you understanding? Sir, the force is applied forward in this. Suppose you also apply it backward. I said, here is the problem. You do this problem for me now. I have applied force forward and also backward. Now tell me all the things. Sir, how much will be the acceleration? Sir, how much will be the tension? And sir, sir, how much will be the tension as a function of x? Sir, how will the graph be plotted? Tension versus x. Your time starts now. Pause the screen, son, and try the question yourself. Okay. Solution. I said, yes. Sir. I said, yes, sir. Sir, this is very easy, sir. Sir, look, what will we write for acceleration, sir? Forward force applied by you is 100. Backward is 40. So pulling force minus resisting force divided by total mass. Sir, this comes out to be six. Okay? Okay, sir. Sir, you need the midpoint, sir. This tension, C, is the midpoint. You need what here? You need tension here. So always remember. I have said this before, whenever you are asked for tension, whenever you are asked for normal, draw its free body diagram. I will draw the free body diagram of the part from A to C. Look here. This is point A. This is point C. I have drawn its free body diagram. Of how much? Of this much. So now tell me, sir, tension will be acting forward, say TC. I said, okay. Sir, force is acting backwards, how much? Sir, 40 Newtons. I said, okay. Its acceleration is how much forward? Its acceleration is how much? Six. And sir, sir, sir, how much is its total mass? Sir, how much is its total mass? Sir, its total mass is 10 kg. So how much will be its mass? They say, 5 kg. So what will you write? You will directly say, sir, forward force minus backward force equals its mass, which is 5 kg, multiplied by acceleration, which is six. So how much will tension at C be? 17 Newtons. This is how problems are done. Are you understanding? Clear? Okay, sir. And if suppose someone asks you, sir, tell us at a general point x, how much will be the tension, P or P, tell me the tension? So do the same thing that you did a little while ago. What? They say, sir, look, sir, how much is the acceleration? I said, the force acting backwards is 40 Newtons. We have calculated the acceleration to be six. Sir, tension is needed here. So why not draw the free body diagram of this much part? I said, okay. Tension will be acting forward here, T. So I am focusing on this much. I am not focusing on the rest. So I say, erase the rest and finish it. Remove it. Remove, remove, remove, remove. Absolutely remove it. Absolutely remove it. They say, okay, sir. Tension at C will be acting forward. So what will you write for this? They say, sir, suppose its acceleration is A in this direction. So you will say, sir, what? I said, forward force minus backward force equals its mass. How much will be its mass, brother? How much will be its mass, my brother? Sir, its mass will be, sir. How much will be the mass of length x? Sir, we just found it. Mass of 10 kg, mass of 10 meters is 10 kg. Understand it like this. Even if some other value was given, you can note this down somewhere. Sir, if the mass of length L is m, then the mass of 1 meter length is m / l. Then the mass of x meters length, my brother, is m / l * x. Because I have given 10-10. It is possible that they might say 10 meters and

The mass of 80 is 50 kg. Okay? So you put 50 here, put the value here. Okay? So what have I written here? They said, "What have you written?" I said, "Brother, I have written its mass." They said, "How much mass is it?" I said, "Brother, the mass is m / l * x. This mass * acceleration. Let's put the values in the question. The mass was 10 kg, the length was 10 kg. Sir, let x remain x. Sir, what is x? Sir, what is the acceleration? It is six. So as soon as you solve it, my brother, the tension at any general point will come out as 40 + 40 + 6 * x. Is that clear? And if someone asks, tell me the graph, then I think you must have understood this. Sir, what is the graph of t versus x now? It has become y = mx + c. The slope is positive, and mx + c is also positive. So its graph will look something like this. What is this, brother? This will be your 40, and where it goes, I think you can do the next question after this. Where it goes, it will go to 100. Tell me, is this clear? Is it clear? So, this question, son, it is very important to do it once. If you do it once, your fear will go away. Okay? Suppose the tension here. Where did this go, brother? At 10 meters. What is the value of the tension? It has become 100. You can verify it if you want. Put x = 10. 60 + 40. That means yes, it is correct. Absolutely correct. Okay? Okay. Let's go, sir. Okay, sir. And and questions. I said, "Yes, absolutely." Now let's do some questions, the lifting questions. It is very important to look at this once. Lifting questions mean lift questions. You will be given language like this in front of you, like the first question. I have written it here. Now you look at it. I have written here that a force is placed. Oh, sorry, a block is placed. I said, "Okay, brother." A block is placed here. I said, "Okay." I want to lift this block. So how much force will I have to apply? So obviously, how much force is acting downwards here? They said, "Make its free body diagram. How much force is acting downwards?" They said, "mg is acting downwards, and normal is acting upwards." So if you want to lift it, what should be the value of f? They said, "The value of f should be greater than mg." Obviously, if you apply less than mg, how will it lift? You will have to lift it more. I said, "Okay." So what is the exact answer? I said, "What is the answer? mg. How much is it, brother?" They said, "mg is 100 here." So the value of f should be greater than 100. How much more than 100? They are saying that even if it is slightly more than 100, your answer will come. Are you understanding? If it is slightly more than f, if the value of f is slightly more than 100, then it will lift. You can make the value of f, sir, 100.0001. It will lift at that too. I said, "Okay." So it just needs to be more than 100, and your block will lift. But we won't write this in the exam, will we? So what do we write in the exam? In the exam, we give the proper answer. So in such questions, whenever an answer comes, remember that we have to give the minimum f as 100. We know that it will not lift at 100, but it will get the tendency to lift. It will not move upwards. It will not move upwards, but the normal will become zero. Sir, how did the normal become zero? I said, "Look, the value of f is 100. mg is acting downwards, which is 100. 100 cancels out. Your normal will become zero." Okay? So at f = 100, listen carefully. In this question, what will we say? That sir, from today onwards, first you should know everything in detail, and then you should know what answer to give in the exam. Sir, technically, it will not lift at 100 Newtons. At 100 Newtons, the tendency to lift will come. At 100 Newtons, the value of normal will become zero. If you apply a force slightly more than 100 Newtons, then it will lift upwards. Its acceleration will be upwards. But in the exam, we will give the answer as 100. Now, in this, he will say, "Brother, I applied f here." I said, "Okay, brother, I applied f here." He said, "Tell me, tell me, I want to lift it." So I said, "What will be the component forward?" They said, "f cos 37." I said, "What will be upwards?" They said, "f sin 37." I said, "If you want to lift it upwards, then make the upward force equal to mg." That means f * 3/5 = 100. 500/3 is the answer. Finished. Are you understanding? Like this question has been changed a bit. Now it has been brought into the function of time. This question is often asked. Children make mistakes. What? He said, "Brother, a force is acting." Okay? And the value of the force is 10, and it is acting at 37°. I said, "Okay." Now he said, "Find the acceleration of the block when it lifts off the ground." He is asking, when it lifts upwards, tell me what will be the acceleration of the block? So often children answer zero. Why? "Oh sir, you are lifting it upwards, so you are making the upward force equal to the downward force, aren't you?" Sir, tell me, when you wanted to lift it upwards, you made the value of F equal to 100, right? I said, "Yes, when it had to be lifted upwards, we made its value equal to this." I said, "Yes." So, the upward force is equal to the downward force. So the acceleration is zero, right? I said, "But it will also have a horizontal component, won't it?" I said, "f is here, so won't a component of f come forward, f cos 37?" Yes, I admit, f sin 37 will come. f cos 37 will also come, my brother. So how can you say that? I said, "Yes, sir." So in this question, there is a slight, slight, slight flavor of silly mistakes, so you have to avoid it. So how will we do it? They said, "Sir, if you want to lift it." I said, "Yes, when will it lift upwards?" They said, "When f sin 37 becomes greater than or equal to 100." It will lift that much. I said, "Okay, brother." Okay, no problem. When? Now he said, "When?" So what is the value of f, brother? The value of f is 10. Put the value. 10t sin 37 = 3/5 = 100. I said, "Okay." So what will t come out to be? t = 50/3. It will lift at 50/3 seconds. Now he has asked. Tell me what? Sir, he asked to find the acceleration. Don't tell me when it will lift. If the question was "When will it lift?", then this is your answer. So I am also writing this. "Find when the block will lift off." When will the block lift upwards? Okay? So you will directly say, "Oh sir, make this force equal to mg. Sir, mg is acting downwards." I said, "Okay, mg is acting downwards." So what will you say? Where did the normal go? "Brother, the normal has just become zero." It has just come into the air. It has just come into the air. Okay, sir. Now he has asked to find the acceleration of the block when it lifts off the ground. So, brother, we have balanced this with this. Who will balance this? No one. So what does this mean? This will give acceleration. You will directly say, "Sir, which force is acting forward?" I said, "Forward is f cos 37, which will be equal to m * a." Now you put the value of f. Actually, you could have found the value of f from here. You could have found it from here. From here. If I talk about here, what is the value of f, brother? It was coming, brother, 500/3, right? It was coming as 500/3. So just put the value of f here. 500/3 * cos 37 = 10 * acceleration a. Whatever the answer comes after this, I hope you can do it. Clear? Okay, in the lifting questions, we also get to see a question like this. He will make this same question into a monkey question. He will say, "Brother, there is a monkey on one side." So you should also practice this question thoroughly. Sir, there is a monkey on one side. The monkey's acceleration is upwards, a. So he is asking, what should be the minimum acceleration of the monkey so that this 10 kg block lifts up? I said, "Oh, like this?" I said, "Yes." So they said, "How will we do it?" I said, "Look, brother, make its free body diagram." Can I say here that the tension is t? Okay, sir. Who will lift this above? Tension. So if you want to lift it, what should be the minimum value of tension, brother? It should be 100 Newtons. If the tension becomes 100 Newtons, then it will get the tendency to lift, because it is a 10 kg block. But he has not asked here. He has asked here. So the question has become, what should be the acceleration of the monkey? This means, do one thing, make the monkey's free body diagram. You find its answer. As soon as you make the monkey's free body diagram, sir, tension is acting upwards. Although friction will act on the monkey, but it's okay, we haven't studied friction yet. Understand with tension. Sir, tension is acting upwards, and mg is acting downwards, which is 50, and the monkey's acceleration is upwards, a. Just as you made the free body diagram, your question is solved. Sir, upward force minus downward force equals monkey's mass * acceleration. Okay, sir. What is the tension? Sir, the tension is 100. 100 - 50 = 5 * a. The acceleration will come out to be 10. Tell me, is this clear? This means the same question might be asked like this. Look, like this. He will place the block here. Okay, sir. He will take another one here, and fix this one below, and tell the monkey to walk here. Walk like this. Same question. Now look, same question. Take this. Okay? So you will say, "Sir, okay, let's do it." Solve it. Look carefully. Let's consider this as 10 kg. Let's say the tension on the person is t. So this t, and this t, so it will become 2t. It will become 2t. If you want to lift this upwards, then the value of 2t should be equal to what, sir? The upward force is equal to the downward force. If you want to lift it, what should be the value of t? They said, "The value of t should be 50." Are you understanding? I am changing the question a bit. Let's say the monkey's mass is 3 kg. So as soon as you make the free body diagram of the 3 kg monkey, tension is acting upwards, which is 50, and mg is acting downwards, which is 30. Okay, sir? And let its acceleration be upwards, A. You will directly write, upward force minus downward force equals mass * acceleration. The acceleration will come out to be 20/3. You will say, "Sir, where is this rope?" It is tied. This rope is tied below. Okay? So like this, I have one pulley. Put two pulleys like this. Put four pulleys. Put four pulleys. Are you understanding? So questions of this type can be asked here. In this, a type of question is being asked, which I have written here. A common question you will see in front of you will be like this, where the diagram is given like this. A mass is placed here, and this is a large pulley, and this is a small pulley. I have taken this and tied it here, and the question is trying to say that f is equal to, suppose, 30. F is equal to, suppose, 30. So he said, "Tell me, when will the 10 kg block lift?" Tell me, when will the 5 kg block lift? I said, "Okay, brother." Let's do it. What's the big deal? They said, "Okay, sir, let's start." First, let's talk about the 5 kg one. I said, "Tell me one thing." Suppose the tension in this rope is t. Yes, sir, it is t. So the tension in this rope is also t, and this will become 2t. Sir, okay, sir. So look, if you make the free body diagram of this pulley, then t is here, t is here, and t is here. Look, there is a rope here, there is a rope here, there is a rope here. This means the tension here will be 3t. They said, "Make the free body diagram?" Massless pulley, ideal pulley. Downward force equals upward force. Downward t, t, so what is the upward force? It has become 3t. Now, if I talk about the solution, brother, I will directly say what? They said, "Sir, when will it lift?" When the value of t becomes 50. Sir, make its free body diagram. Upwards t, downwards 50. When the value of t becomes 50. Okay? I said, "Okay." And sir, what is known from here? Sir, what is the tension in this green rope? It is 3t, which will be equal to what? They said, "30t." It will be equal to 32. Brother, the force with which you are pulling this upper rope upwards, that much tension will develop in it. Okay, sir? So I said, "Put the value." So look at the question. Sir, 3 * what is the value of t? It is 50. Equal to 30 * t. So here, what will t become? Sir, t will become 5 seconds. And if someone asks you, tell me, when will the 10 kg block lift? Then what will you say? They said, "When will the 10 kg block lift?" When 2t becomes equal to what? Sir, 2t will become equal to 100. Why? Sir, to lift it upwards, a force of 2T is acting, and mg force is acting downwards. Until the upward force is not greater than or equal to mg, it will not even think about lifting. So what is t from here? They said, "Sir, t from here has become 50." And what did we get from here? Sir, 3t is coming, that 30 * t. Sir, 3 * 50 = 30 * t. Oh sir, t has also come out to be 5 seconds. This means in this question, both your blocks will lift together. Tell me. Is this clear? Okay? So, these were some different profiles of questions that I have done for you here. So, you can do one thing. Pause the screen, son, and all the children should note down these questions. Okay, brother, let's move towards our next part, which is called spring force. Sir, spring force means? I said, "Brother, you must have seen." For example, if I say, appearance, we call this a spring. Okay? This is not an ideal spring. But first, let me tell you about the ideal spring. What properties should a spring have in Newton's motion? So, in Newton's law of motion, the string we use, first of all, it should be massless. It should have absolutely no mass. Okay? After that, massless? They said, "Sir, mass, it's not like that, is it? It will have mass." I said, "Yes, it will obviously have mass, but its mass is so small that we can neglect it." Okay? Okay, sir? Okay. After that, sir, the pitch, what is the pitch? They said, "Sir, suppose I make a spring here." So, sir, the ideal spring that we have to study. So, sir, this distance, this distance, this distance should be the same. That is, I said, if you make a spring like this tomorrow, like this spring, we don't have to study this. Okay? We don't have to study this because this is, in a way, not an ideal spring. So, I have written everything here in advance to save time. Suppose there is a natural length of a spring. I say, suppose the spring is like this. I have not applied any force on it. I have just kept it like this. Are you understanding? I have not applied any force on it. I have just kept it like this. Neither did I stretch it nor compress it. So its original length, its actual length, its relaxed length, its natural length, is called, my brother, what? I have used all these terms in four or five terms for the same thing. For example, let me repeat. Then I have not applied any force. Now its length, we will call it natural length. I have not applied any force. I have just left it in its state. Okay? Okay, sir? I have not applied any force. I have just left it like this. So we will call it natural length. Or relaxed length. This spring is relaxing. Or original length. Okay? Now, if after this I stretch it or compress it, first let me show you the demonstration of stretching. Suppose I said, I have compressed it from here. Okay? I have, sorry, I have fixed it from here. After fixing it from here, now I am pulling it like this. I said, "Okay, brother." I have held it from here and pulled it like this. So as soon as I pull it like this. Now look carefully. As soon as I pulled it, what happened? Now this spring is trying to retain its old position somewhere. I am feeling it. Okay? Earlier, the spring was in its relaxed state, in its natural state. So what happened? It was happy in its state. It was stable there. I grabbed it and pulled it. I developed elongation in it. So what happened is, as soon as I grabbed it and pulled it, somewhere I tried to disturb it. Somewhere I increased its bond structure. Like it used to happen in a rope. So as soon as I grabbed it and pulled it. This means the spring is now disturbed. The spring wants to regain its old position. The spring wants to regain its old position. The spring wants to move towards its natural length. So, brother, to regain its old position, the force that it applies on my hand, the force that it will apply on this hand of mine, what will we call it, my brother? Spring force. Now you will say, "Sir, where is it applying force?" I said, "I am feeling it, isn't it applying force?" This spring is holding my hand and pulling it back. I am feeling it. Look, as soon as I leave it, as soon as I leave it, look, it will run backwards. Are you understanding? As soon as I leave it, where will it run, my brother? It will run backwards. This means it wanted to regain its old position. So, yes, sir, if you disturb the spring, if you stretch or compress the spring from its natural length, then the spring will apply force. Force? Okay, sir. So, suppose in this question, I have stretched the spring by x from its natural length. So can I say that the spring will apply force? Yes, sir. This force will be applied. Sir, in which direction is this force applied? I said, the force is applied towards this vertical line, which we call the natural length. So this means the force applied by this spring.

This is called spring force. When will it apply force? Either the spring is stretched or the spring is compressed. If you compress the spring, it will apply force backwards. If you pull it, it will apply force forwards. Are you getting the point? Yes sir. Now the question is, sir, this force has come. So there are two important things here. What? You say sir, force is a vector quantity. So what will be its magnitude? How will we take its direction? So I said, let's first go to the magnitude. So Hooke's Law told us, we will study this in detail in elasticity. Hooke's Law told us that the spring force is directly proportional to X. Meaning, the more you stretch it, the more spring force will be applied. The greater the value of x, the greater the spring force will be. So, can I say here that sir, f spring will be equal to k * x? As soon as we remove this proportionality, a term comes here, what is its name? It is k. I said, okay. This k is what we call the spring constant. What do we call this k, my brother? Spring constant. Are you understanding this? Is it clear? Yes sir. This f spring is proportional to x. As soon as we removed it, a constant came, which we call the spring constant. Its value will be given to us. This means we understood that if you stretch the spring by x or compress it by x, then the value of the spring force is k * x. Now the question is, sir, what is x in this? I said, look brother, in this, x is either elongation. Elongation is fine, compression is also fine. What is x in this, my brother? Either you call it elongation or what do you call it? Compression. Sir, from where? I said, from the natural length. This is very important. From the natural length, how much have you stretched it? Are you getting the point? How much have you stretched it from the natural length? This, brother, is basically the story behind it. How much have you stretched it from the natural length. I said, okay, brother. Okay. Now this is your magnitude statement. If someone wants to write it properly in vector form, we write it like this: f spring = -k * x vector. You say, sir, I have applied it forcefully. I said, look brother, the minus is applied like this: if I stretched it, you say, yes sir, stretched it, sir. First, this point, now understand it like this. First, this point of the spring was here. You say, yes sir. I stretched it and took it here. Yes, guru. So what did I do? You say, sir, you stretched it from here to here. How much did you stretch it? You say, x. I displaced it forward. So where did the spring force act? Backwards. x vector is forward. So where is the spring force acting? Backwards. That's why I had to put a minus here. Similarly for this. Let's assume in this case I took it here. I attached a block. I compressed it here. So for this, x is in this direction. This is your x. I said, okay, brother. And the spring force is in the forward direction. So x and spring force, both became opposite to each other. So that's why we put a minus here, my brother. Is it clear? So listen to me today. The main point is this. First of all, remember this thing. F spring = k * x. Is it clear? k * x. What is k? Spring constant. What is x? Either elongation or compression, anything is fine. Elongation is fine, compression is also fine. Meaning, if the spring is stretched by x, it will apply kx force. If the spring is compressed by x, it will also apply kx force. And sir, where will it apply force? How will the direction be? I said, take the direction with the feeling. You say, with feeling, what do you mean? I said, tell me yourself. If I hold it like this and pull it, in my opinion, where is the force acting? Inward. And if I compress the spring like this, in my opinion, where will the force act? In this direction. End of story. Just catch this thing. You can see this with feeling. After this, your questions will be ready just like they were before. For example, I have put a question here. I have taken three questions here. I said in these three questions, brother, tell us what will be the value of the spring force if the block is in equilibrium? You will say, sir, look, how much force is acting downwards on it? I said, brother, the force acting downwards is mg. Sir, so what should I write here? F spring will be equal to what? I said, brother, it is in equilibrium. Brother, this mass is in equilibrium. mg is acting downwards. Who balanced it? The spring. So what will be the value of the spring force? Sir, the value of the spring force will be m * g. Sir, the spring force was kx, brother, it is also kx. If it asks you for elongation, if it tells you its spring constant is k, then tell me how much it would have stretched from its natural length? Then you will say, sir, F spring = kx. This means you will directly say mg = kx. End of story. Are you getting the point? Here both questions are done together. The block is in equilibrium. So how much force would the spring have applied? You will directly say, sir, how much? mg. So the value of the spring force is mg. So one question is this. Another question will be, brother, tell us what is the elongation in the spring force? Sorry, what is the elongation in the spring? Are you getting the point? And what is the elongation in the spring? Then you will say, sir, look, it's a simple matter. Do nothing, find the spring force, and equate the spring force to kx. Got the point? Okay sir. For example, if I talk about this. Sir, tell me, sir, tell me here, what will be the spring force and what will be the spring force here? So, just like we were doing before, do it like that. What will be the spring force here? Sir, draw its free body diagram. Okay? mg is acting downwards. What is acting upwards? Spring force. So, what will be the spring force, brother? mg. Sir, what will be the spring force here? I said, the spring force here will be. How much is downwards, sir? 3m. So, what will it be, brother? This 3mg. Hey, hold it. Hold it from here. How much weight is hanging downwards? You say, 3m. You say, done. Sir, so it's like in tension. Yes, but there is a difference between tension and spring. You say, what is the difference? But a rope always pulls. A rope never pushes. But a spring pulls and pushes. That's the only difference. As long as it is the case of an elongated spring, it is like tension. Oh sir, yes, you can also compress a spring. But you cannot compress a rope. That's the only difference. So tell me, if I ask you here. I said, tell me, what will be the value of f spring here? You will directly say, sir, it is kept in equilibrium by 3mg. So 3m is kept in equilibrium. So 3mg. I said, tell me, what will it be in this? You will directly say, sir, 3m and m, that's 4m. So it means 4mg. I said, tell me, brother, what will be the value of f spring here? You will say, sir, 3m, 4m, and these three, three, 3, 6mg. I said, tell me, what will be the value of the spring force here? You will directly say, sir, mg sin theta is acting here. Done. Are you getting the point? Okay, yes sir. Okay. Now, for example, I am taking a question here so that things become better understood. I have written in the question here that, brother, understand carefully. This is a block of 2 kg and 3 kg. A force of 100 Newtons was applied to the 3 kg block. I asked, tell me what will be its acceleration? Okay? Okay sir. Its acceleration is given as 10. Okay sir. So you will say, sir, do one thing, sir, draw the FBD of the 3 kg one. Draw the FBD, brother. What will you say, sir? 100 is acting forward. Sir, suppose the spring is stretched, so f spring is acting backward, and because of this, its acceleration is forward, 10. What will you write? Equation: Sir, forward force minus backward force equals mass * acceleration. The value of the spring force is my brother, 70. Is it clear? Okay sir. If I draw the FBD of 2 kg, because he asked for acceleration, so if the spring is stretched, it will be applying force here, it will be applying force forward. This means f spring is acting forward, whose value is 70, and its mass is 2 kg. This means if I ask you its acceleration, then sir, only one force is acting, 70. Mass is two. 70 / 2 will come out to be equal to 35. This means you have calculated the acceleration. You have calculated the spring force. Now, if I ask you for the elongation in the spring, then you will directly say. You say, sir, what is f spring? My brother, f spring is 70. Sir, if the value of the spring force is 70, then equate it to kx. So here, its value of k is given as 100 * x. Solving this, x will come out to be 70 cm. Such questions are basically asked. Are you getting the point? Okay, listen to this. There is another method for this. Method number two. You say, what? I said, if I consider the whole thing as a system. I considered the whole thing as a system. Yes sir. Then the only external force is 100. So we see a slight modification of Newton's second law, that f net can also be written as m1a1 + m2a2 + m3a3 + m4a4. Multiply the masses by their accelerations with proper vector signs. Okay? Okay? So f net = m1 + m2 + m3. This was it. So, sir, let's apply this. I said, the answer comes in just one line from this. What is f net, brother? 100. The external force is 100. m1 a1. What is m1? Three. What is the acceleration? 10. Plus m2 a2. What is m2? Two. What is the acceleration, my brother? a2. So as soon as you solve, a2 will come out to be 35. See, the answer came out in just one line from here. Got the point? Is it clear? So, my brother, this is spring force. Now, for this, we do the most detailed analysis of the spring in SHM. Simple Harmonic Motion. A chapter will come later. There will be plenty of springs in it. For now, in Newton's Laws of Motion, you should be clear about this. What should be clear? That, brother, tell me what is the value of the spring force here and how does the spring force act? That is the important part. After this, let's move on. Hold on for a minute. Yes. After this, there are some small questions. For example, I am writing here, which is called spring cutting. That we have cut the spring. So you often get questions like this in front of you, that brother, there is a big spring, it has been cut. Cut into two pieces. So tell me, what will be the spring constant of the individual pieces? Tell me the value of the spring constant individually. You say, what do you mean? I said, what I mean is, for example, if I ask you a question. I said, what? Suppose this was a big spring. I said, okay, brother. You cut it into two pieces. You cut it, my brother, into two pieces. You say, cut into two pieces, what does that mean? I said, brother, see, understand it like this. Suppose this is some spring. Okay? This is some spring. This is some spring. This is some spring. This is some ideal spring. This is some spring. Okay? What did I do? I cut it into two pieces like this. These pieces. These are its two pieces. So tell me, what will be its spring constant? Tell me, what will be its spring constant? This is basically, my brother? A question. So we will see its detailed version in the elasticity chapter. For now, just remember this much. You say, what? You say, sir, sir, if the material is the same, then the product of K * L is constant. That's it. Just catch this much. Remember this much, that the material is the same. The material did not change, did it? You cut the spring, so the material did not change, did it? The material is the same. If it's an iron spring, it will remain iron. If it's steel, it will remain steel. It's not like it was steel, and after cutting, brother, it became gold. Are you getting the point? So if the material is the same, then you will directly say. The product of K * L, its K1 * L1 product, and its K2 * L2 product, sir, remains the same. It is a constant. This is the concept behind it. Why is this so? We will study this in elasticity. For now, just remember this line. I said, okay, brother, only this much. Just one term. For example, if I give you a question. I said, tell me. I cut it into two pieces. So what will you write? Sir, tell me the values of k1 and k2. You will write k * l = K1 * 6 = K2 * 5. Like this. Okay? So what will K1 be from here? K1 will be 1000 / 6. What will K2 be from here? 1000 / 4. Equate this to this. Solve and get the answer. Okay? If I ask here. I said, brother, I made three pieces of it. You say, three pieces can also be made. I said, yes, brother, you can also make three pieces. Suppose I say as an example, brother, this is our spring. Okay? This is suppose a 10-meter spring. I made three pieces of it. I cut it here, and I cut it here. Okay? Yes, brother, the spring has rested in peace. Okay? So now, if I ask you, sir, we have made three different pieces of a spring. One here, one here, and one here. Now tell me, what will be their individual spring constants? So what do you have to do? You have to function the product of k * l. You will say, here k is 100, l is 10 = k1 * 5 = k2 * 3 = k3 * 2. End. Solve it afterwards. Got the point? Is it clear? Okay? So, brother, questions like this are asked in this. Now, suppose there is one more small statement here. If I have broken a spring into two equal parts. We have broken it into two equal parts. Sir, there is a spring constant, we have broken it into two equal parts. I said, okay, brother. So tell me, so what will you write? k * l = Sir, let me write this as small l here. k * l = k * l / 2 = suppose its spring constant is k1. k2 * l / 2. I said, okay, brother. Okay. As soon as I solve this from here, sir, l / 2, l / 2, l cancels out. What will k1 be equal to? It will be 2k. And what will k2 be equal to, my brother? Two. Are you getting the point? Okay? Meaning, if you break a spring into two equal parts, then the spring constant of the individual spring will be twice the spring constant of the larger spring. If you break it into two pieces, it will be double. If you break it into three pieces, the spring constant of the individual spring will be three times. If you break it into four pieces, it will be four times. If you break it into 10 pieces, it will be 10 times. If you break it into n pieces, it will be n times. Got the point? Is it clear? Okay? After this, there is one more small article here. This article, you can skip it if you want, because we study this article in more detail in SHM. What? You say, sir, suppose you have attached a block to two springs. Two or more, and they are in parallel. These two are also called parallel. So k equivalent, after solving mathematically, comes out to be k1 + k2. Are you getting the point? And if two springs are connected in series like this, and I ask you, tell me, if I remove these two springs and want to attach one spring, what should its k equivalent be? Then you will say 1 / k equivalent = 1 / k1 + 1 / k2. Similarly, if there were four springs, you would write 1 / k equivalent = 1 / k1 + 1 / k2 + 1 / k3 + 1 / k4. Meaning, as you can see here, your results in series are the opposite of resistance. In resistance, what happens? In series, we add them as they are. Okay? And in parallel, we add them by taking the reciprocal. So the same thing is here. It's just the reverse. What used to happen in series with resistance, happens here in parallel. And what used to happen in parallel with resistance, happens here in series. This means I will directly say, just remember this much, that the results here are the opposite of resistance. If someone asks you, sir, there are four springs. Four springs are in series. So tell me, what will be k equivalent? Then 1 / k equivalent = 1 / k1 + 1 / k2 + 1 / k3 + 1 / k4. Are you getting the point? Suppose, sir, there are four springs in parallel, k1, k2, k3, k4. So tell me, what will be f equivalent? k1 + k2 + k3 + k4. End. Don't you get the point? This, my brother, is it. But its use in NLM will not be much. Very rarely, suppose it is used in detail in the chapter of SHM, Simple Harmonic Motion. Clear. Still, note it down. After this, let's move to an article on which very few questions have been asked. Only one or two questions have been asked. Even in advanced, only once.

You asked about this. Okay? Listen carefully, what is it? They said, "Sir, look, suppose this entire system is in equilibrium." I said, "Okay, brother, it's in equilibrium." So if I ask you what is the value of the spring force here. You will directly say, "Sir, it will be 2mg, and the tension here will be mg." Okay? "Okay, sir." Okay. Now, if I say that I cut this spring at t=0. I cut this rope. Sorry, I cut the rope, not the spring. Okay. "Okay, sir." Okay. So tell me, what will be the acceleration of a and b? I'll write the question itself: Find the acceleration of a and b after t=c, meaning the string is cut. Are you getting the point? This means the question will be given like this: The entire system is in equilibrium. Now we have cut some spring or rope. Suppose I cut this rope. They said, "Yes, brother, you cut the rope." They said, "You cut the rope, so tell us now what will be the acceleration of each block?" It's very easy. You just need to catch one line here. They said, "Sir, what?" I said, "Look, did you cut this rope?" "Yes, sir." So you cut the rope, so throw it away. Now tell me, what will happen? Will this mass fall down? They said, "It will fall down." So what will be its acceleration? Don't say zero. Okay? Its acceleration will be g downwards. Here you go. Any problem? They said, "This became easy." I said, "Yes, now let's talk about a." They said, "Tell us about a, how will it happen?" I said, "Now do one thing, if you want to know the acceleration of a, first draw the FBD. Draw the FBD. See, brother, how many forces are acting? Divide by mass." They said, "Yes, sir, you are telling the truth, sir." So tell me, if I draw the FBD of a, then what force will be acting downwards first? They said, "mg." What will be acting upwards? "Sir, the spring force is upwards." Just remember this line: the spring force is a sluggish force, an lazy force. It doesn't change suddenly. "Meaning, sir, as soon as you cut the rope. Just before cutting the rope, how much was it acting?" They said, "2mg was acting." So even after cutting the rope, just a little while later, at t=0, how much will it act? It will still act 2mg. This is the most catchy point here. "Sir, the spring is a sluggish force, a lazy force. It doesn't change suddenly." We will study this later. It is a non-impulsive force. I said, "Okay, brother." Okay. So now, as soon as you cut the rope, now hold it, brother. Hold it, the mass. Hold the block. So if you want the acceleration of the block, draw the FBD of the block. "Yes, sir." mg will be acting downwards. "Yes, sir." What will act upwards? The force on it. How much? As much as it was acting a little while ago. How much was it acting a little while ago? But a little while ago, 2mg was acting. So how much will it act now? It will still act 2mg. The story ends here. Now its acceleration will be 'a' upwards. So what will you say for acceleration, sir? The upward force minus the downward force divided by mass m. So what will its acceleration come out to be? Is the question solved? Did you get the point? So this means the acceleration of this block is g upwards. The acceleration of this block is downwards. Suppose I gave you a question like this. I said, "Suppose, tell me, what is the value of the spring force here?" You will say, "Sir, it is 2mg." I said, "Okay." I said, "Tell me, what is the value of the spring force here?" You will say, "Sir, it is mg." Why? Because it is in equilibrium. I gave it in the question. Suppose I said, "Brother, I cut the lower spring in this. I cut it." So, brother, as soon as you cut it, this spring is gone, right? What is cut is dead. "Yes." So, sir, this question became the same as it was a little while ago. Huh? This question became the same. Sir, this will fall down with a=g. I said, "Okay." And this will go up with a=g. This question is the same as what was done a little while ago. This question is solved. This question is the same. Look, spring, block, empty space, and block. It also became spring, block, empty space, block. Yes. The fun will be when I tell you that this time I cut this one at t=0. At t=0, I cut this spring. So tell me, sir, what will be the acceleration of a and b? So let's find the acceleration of a. You will say, "Sir, draw the FBD. What force will be acting downwards? mg. And what force will be acting downwards? Oh, the spring force." I said, "How much?" They said, "As much as it was acting a little while ago." How much was it acting a little while ago? They said, "mg was acting." So this means, what will be its acceleration and how much? They said, "Sir, its acceleration will be downwards, and the acceleration of A will be: What is the total downward force? mg + mg = 2mg. And divide by mass. This will come out to be 2g." And similarly, if I talk about whom? They said, "Talk about the b person." You will directly say, "Sir, how much force is acting downwards? My brother, mg is acting downwards. And how much force will act upwards? My brother, the spring force will act upwards, whose value is how much?" I said, "Whose value is, my brother, as much as it was a little while ago. How much was it a little while ago? It was mg. So how much will it act now? It will still act mg." And upwards mg, downwards mg. I said, "Yes. So what will be the acceleration at p?" "It will be zero." Clear? This is how it is done. Now, do one thing. Suppose I have given this question. If I cut this spring at t=0, then show me the acceleration of a, b, and c quickly. This was initially in equilibrium. The value of the upper spring force was 3mg, the middle one was 2mg, and the lower one was mg. I cut the middle spring. So tell me the value of the acceleration of a, b, and c quickly. I cut this. So what is cut is dead. Let's start with A. "Sir, if I talk about the A person. What force will be acting downwards? mg. Upwards, the spring force. How much? As much as it was a little while ago, 3mg. So what will be its acceleration?" "Sir, upwards 3mg, downwards mg. So the net is upwards 2mg. So its acceleration will be 2g upwards." "Okay, sir." "Talk about P, sir." "mg downwards. Okay, sir." "And the spring force downwards, which is how much? mg." "Okay, okay, sir." "This means what will be its acceleration downwards?" "2g. Why? The total became 2mg." "Make the FBD of c." "mg downwards. Upwards, the spring force. Upwards, the spring force. Upwards, the spring force. How much? As much as it was acting a little while ago." "This means what will be its acceleration?" "Zero. Because the downward force equals the upward force." Clear? Did you get the point? If you understood everything, then brother, type "Yes sir" in the comment box below. If any spring question comes, we will nail it. What is the important thing? If the spring is stretched by x, it will apply kx force. If it is compressed by x, it will apply kx force. And it does not change suddenly. In spring cutting questions, you will directly say, "Sir, the spring will apply as much force just after cutting as it was applying just before cutting." It will not always apply that much. After some time, this block will go up. So the spring will start to compress. It will start to compress. Meaning, the length of the spring will start to decrease. So the spring force will start to change. Look, after some time, just after t=0, it will remain the same. Clear? It is cut at t=0. So at t=0.0001 seconds, it will remain the same. If you ask after 5 seconds, it will change. After 10 seconds, it will change even more. Clear? Note it down quickly, son. Okay, brother, now let's move to the next part, which is called pseudo force. Before going to pseudo force, I am giving you a small question. If possible, brother, try this question now, so that when we study pseudo force later, it will have its own different kind of fun. They said, "What is the question?" Due to less space, I am only drawing the diagram here. I am not writing the language, but I will say it verbally that the language is given like this in such questions. They said, "Okay, sir, how?" I said, "Brother, the question will be given like this, brother. This is your car. What is it, brother? A car. Okay, sir, it's a car. Okay." I said, "Okay." The car's wheel should be on the ground, brother. Here it is. Okay? "Okay, sir." This car is going forward, and its acceleration, my brother, is how much? They said, "What is its acceleration, brother?" It is 'a'. Okay. Okay. Now, what is inside it? We have tied a rope. The pink rope is like this. Okay? This pink rope is tied like this. Here we have placed its mass. Meaning, we have tied the mass with a rope here. Okay? "Okay, sir." Okay. Okay. Let's make it a little bigger, a little smaller. It became too big. Right? I said, "Brother, there is a mass here, and I have connected it with a rope like this, in this manner, and I have fixed the rope here. I have fixed the rope here, my brother. So, as you can see from the diagram, if I draw a vertical line here, the angle the rope has made with the vertical is visible in the diagram, it is angle theta. The question is that theta is constant. What is theta, my brother? It is constant. So tell us." They said, "Find." They said, "What do you want to know?" I said, "Brother, tell us, what will be the value of theta?" Find theta or find tension or everything. What is its mass? The mass of the block is m. The language of the question will be something like this: There is a car which is moving in a horizontal plane with acceleration a, and there is a string. There is a string attached with a mass m, is fixed at the ceiling of the car. Okay? I fixed the rope. Where? At the ceiling of the car. I said, "Okay." Such that, now it will say, such that the angle made by the string with the vertical is theta, and it is constant. And it is constant. Meaning, you will have to visualize this thing that the story has become something like this, brother, that I have, I have, I have, I have, I have. Suppose this is the rope. This is your rope. So the rope is like this, and there is a mass here. So this means it is going like this, like this. The car is going forward with constant acceleration, and brother, it is not moving anywhere. It is at rest with respect to this. It also uses words like this. It also uses words like this. What did you say? Mass is at rest. Mass is at rest. I also use these words here. Okay? Mass is at rest. With respect to the car. Now look, if you see it with respect to the ground, the mass is not at rest. With respect to the ground, you will see the mass moving forward. But he said that brother, the mass is at rest with respect to the car. This means that whatever acceleration the car has, that much acceleration is of my brother, the mass. So find theta and t. You will say, "Sir, how to do it?" I said, "Solution, come, let's talk. How will you do it?" You will say, "Sir, the best thing is, sir. Draw the FBD and solve it." I said, "I am removing this mass for a while." "Okay, sir, draw the FBD, sir." "First, what will you show downwards?" "Sir, we will show mg downwards." I said, "Okay." "Sir, what will you show here?" They said, "Here we will show tension t." I said, "Very good." So if I draw its FBD, you will say, "Sir, mg is acting downwards. And sir, tension t is acting here. And this is your green mass." I said, "Okay, sir, do one thing. Does this mass appear to be flying in the air to you? Does it appear to be going upwards? No. Does this mass appear to be going downwards? No. Does this mass appear to be only going forward?" Yes. They said, "How?" I said, "Look, like this. Focus on it. I'm making it red because green is not visible. I'm making it red. Focus on that mass. Look, when this car is going forward, look here, as soon as this car is going forward, look, this mass is neither going up nor down. This mass is only and only going forward. Are you getting the point?" They said, "Yes, guru ji. Tell me once more." I said, "Once more, look. I am taking it forward. Look, I am taking it forward. Look, this mass is neither going up nor down. Where is it going? This mass is only and only going forward." I said, "Okay. So does this mean I can say, sir, this mass is in equilibrium in the y direction?" "Yes, you can say that. It's not going up or down." So does this mean I can say, sir, it is in equilibrium in y? Upward force equals downward force. "Sir, the angle is theta, so this angle will also be theta. If this is theta, then this will also be theta." The upward component of t will be, my brother, t cos theta. The forward component of t will be, my brother, t sin theta. You will directly say, "Sir, what will you say?" "Sir, it is in equilibrium, so the upward force equals the downward force." I can write here, t cos theta will be equal to mg. I said, "Okay." I said, "Good. Now when talking about x, forget the brother. Do you feel that its acceleration is 'a' forward? Do you feel that the acceleration of this mass is 'a' forward?" They said, "Yes, sir. The acceleration of this mass is 'a' forward. You are absolutely right, sir." Why? The entire car is going forward with 'a'. If you don't see it, look again. Look, this. Look, the car is going forward. So look, this mass appears to be going forward with A. So, brother, if its acceleration is 'a' forward, then due to what? What is the force that is providing acceleration? They said, "Sir, which one is left?" "Draw the FBD, you will see." "Sir, sir, look, mg is downwards. This is not it. Sir, a component of T is upwards. This is also not it. Which one is left? T sin theta." So does this mean I can say that tsin theta has provided acceleration here, which is equal to? They said, "ma." If I take the ratio, then tan theta will come out to be a/g, or a will come out to be g tan theta. Brother, do you understand this point? Okay? a is equal to g tan theta. Some students also remember the result because it is such a standard question. It has been asked so many times in examinations. Mains people keep asking it shamelessly. So you will directly write a = g tan theta. Tell me, do you understand this point? Clear? Okay, sir. So, sir, why did you bring this suddenly? I said, "Why did you bring it?" Let's move to the next article and then come back to this question again. Okay, someone will say, "Sir, what will be the tension?" I said, "You can find the tension from here." Square both of them. Add the square of this and the square of this. So it will be t² = ma² + mg². So t will be equal to the square root of m a² + b². Okay? Okay. Let's go, sir. Now let's move to the next part, which is called pseudo force. They said, "What is pseudo force?" I said, "Brother, understand carefully." Okay? Until now, what we basically study in Newton's laws of motion, I'll clarify first. We study tension force. We study mg force. We study, we study, spring force. Okay? We study, normal force. Okay? Similarly, there is one more force, pseudo force. Understand carefully. Often, many students remain confused about this. Okay? Understand carefully. They said, "What is pseudo force?" I said, "Look." They said, "Yes, sir." I said, "I said, there is a lift here." "Okay, brother?" Okay, it's a lift. Okay? "Okay, sir, it's a lift." Inside the lift, I have placed a block here. Red colored. Is that clear? Okay. "Sir, a red colored block is placed inside the lift." What is its mass, brother? Let its mass be m. The lift is going up with acceleration a. Any problem? It could be a lift, or it could be, brother, that they clean up the entire upper structure and write directly, brother, this is a platform, this entire platform is going upwards. Now if you add the ceiling, it will become a lift again. Okay? So what is this case, my brother? This case is the same. They said, "Okay." They said, "Sir, what do you want to know?" I said, "We want to know." They said, "Sir, find the normal contact force between the block and the lift." "Okay, sir." According to the physics you have studied so far, you will say, "Sir, this is the ground." I said, "Okay, brother." "And you are standing on the ground and looking at it." I said, "Okay, brother?" "You are standing on the ground and looking at it." They said, "Okay, sir." So what will you say? "Sir, I am solving it here." You are solving it with respect to the ground. With respect to the ground, with all the physics you have studied so far, you will say, "Brother, sir, do one thing, sir. Draw the FBD, sir." "We always used to draw the FBD for normal tension." I said, "Draw it, brother." So this person looked at this block. This person said, "Brother, see, the mass of this block is m." I said, "Okay, brother." "The mass of the block is m, so can I say, sir, that the force is acting downwards on it, mg?" I said, "Okay." "Can I say, sir, that the force is acting upwards, normal?" "Yes, sir." "Can I say, sir, that when we saw it from the ground, it appeared to us to be going upwards with acceleration a?" They said, "Yes, sir." I'll draw the ground part here. Hold on for a minute. I'll draw the ground part here. And how do things appear to us, my brother? 'a' downwards. Yes, downwards. Flying upwards. Things appear like this to us. I said, "Okay, brother." "Look at it calmly from the ground." You are looking at it from the ground. Okay, okay, sir. Meaning, we are solving the question, my brother, with respect to the ground. So what will this person say, brother? This person will say, "Sir, draw the FBD of this block." "You see, normal is acting upwards." [Applause] "Okay, normal is acting upwards." "mg is acting downwards." I said, "Yes, brother. We are looking at it from here." Okay? So what will you say, sir? "Normal is acting upwards. mg is acting downwards." "Sir, there is acceleration." So we will write: upward force minus downward force equals mass times acceleration. So the value of normal will come out to be, my brother, mg + ma. This value of normal will come out to be mg + ma. "Okay, sir. No problem. It's a very good question. Absolutely correct. Nothing new in the question." I said, "Brother, the problem arose." They said, "When did the problem arise?" I said, "When, for this same question, yes, brother, a person said that I will solve it by sitting inside, inside the lift." I said, "You can do that, brother." So someone went inside. I said, "Okay, brother." He said, "Brother, here, let's do one thing, sir." They said, "I will solve it by sitting inside." I said, "You can do that." So for a while, you become this. You went inside the lift, right? They said, "Yes." So for you, my brother, the world has now become this. Look, this is your life. Meaning, your world has now become this. This, this, you can't see anything outside. You can only see this. Can you see? You can see, brother. You can see the block. You are inside the lift. You can't see the outside world. You won't see it. Brother, if you go and sit inside the lift, the lift is closed. What is happening outside? How would I know? You must go to watch movies, go to cinema halls, etc. Whenever you go to movies, the cinema hall is on the fourth floor. Okay? And we have gone to the ground floor, so we pressed the lift button. So when we are going up, okay? So we don't know what is happening outside, do we? For us, that is the world. For us, that is the buffer, that is the ceiling. Are you getting the point? For us, and for all those who live in multiplexes or all those who have used the lift, you must have seen this. What do you see? What does the outside world mean to you? You have gone inside. I said, "Yes. Now when you went inside." I said, "Okay, brother." "Now when you solved the question, brother, what will you say first?" You will say, "Guru ji, look, sir, I am solving it by sitting inside." I said, "You can do that, brother." You will say, "Sir, look, mg is acting downwards." I said, "Absolutely correct." "And sir, normal is acting upwards." I said, "Absolutely correct." So, brother, he said, "Sir, mg is acting downwards, normal is acting upwards." So this person said, "Sir, I see this block is stationary." So when we solved it with respect to the lift, you will directly say, "Sir, upward force equals downward force." "Sir, why did he say that?" I said, "Brother, ask him. For a while, you become him. You go and sit inside." "Go, you sit inside." 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It has arrived. A mistake has been made in it. Are you understanding? So, in short, we went into the frame of the lift. When we applied Newton's Law of Motion in the frame of the accelerated lift, it failed. Newton's Law of Motion failed, my brother. Clear? It became invalid. So, a huge uproar began. Because, brother, we had gotten the three laws with great difficulty. After that, if such an uproar happens, how will it work? Then, brother, what should we do? Sometimes, if something in the house gets spoiled, we don't replace it. We don't replace it. We first try to repair it. If your mobile is slightly damaged, you won't say, "Brother, it's broken, let's finish it, I'll buy a new phone." No, you try to get it fixed. So, in exactly the same way, in exactly the same way, people thought, "What should be done?" They said, "Here, Newton's Law's honor is in danger. What is Newton's Law? It has gone wrong in this frame. It has become invalid within this frame." So, a frame where Newton's Law of Motion is not valid, we call it a non-inertial frame. And a frame where Newton's Law of Motion is valid, we call it an inertial frame. Are you understanding? So, the way to remember it is, sir, where Newton's Law is not valid. Where is it not valid? Sir, inside the lift. Like inside an accelerated lift, or like inside an accelerated car. Are you understanding? Any person who has acceleration. Any person who has acceleration with respect to the ground. Any person who has acceleration. Whether it's the lift going up with acceleration, the balloon going up with acceleration, the wedge going forward with acceleration, the block going forward with acceleration. Any person who has acceleration. If you are sitting on it and solving the problem, it means you are in a non-inertial frame, and in a non-inertial frame, Newton's Law of Motion is not valid. Clear? And if you are solving on the ground, standing on the ground and solving, or if you are sitting on a person whose acceleration is zero. Acceleration is zero. Okay? Acceleration is zero, so there is no problem. So, what do we call it? An inertial frame. Anyway, we will get to that later. First, understand it like this: this Newton's third law, sorry, Newton's law got stuck. First, let's pick it up. They said, "Brother, how do we fix this?" So people thought, "Brother, how do we fix it? How do we fix it?" Then some people came. They said, "We will fix it. But don't ask us what, why, or how we are doing it." They said, "Okay, brother." They said, "Brother, you fix it. Just our Newton's Law is broken. Fix it." So they said, like village mechanics. You have a mobile phone. Your mobile is finished, your mobile is broken. You go to the mobile guy. He might have passed 5th or 6th grade, but he fixes your mobile. Right? Even if you have done a big B.Tech engineering, you don't know the small things inside the mobile, what this is doing? What this is doing. But that boy who has passed 7th or 8th grade fixes your mobile. He changes the display. Okay? Okay? He also tells you the internal faults. He cleans it, and if some IC is faulty, he replaces it. Are you understanding? So, in the same way, some mechanics came. They said, "Look, brother, we will fix your Newton's Law. Just don't ask us why we are doing it." They said, "Okay, brother." So they said, "Whenever you are sitting in an accelerated frame, or sitting inside an accelerated frame, or sitting on an accelerated frame and solving a problem, add an extra force. m * a, where m will be the mass of the block." I said, "Okay, brother, mass of the block into acceleration of the person." I said, "Okay, brother." They said, "Sir, give an extra force." I said, "Why?" They said, "Don't ask, just give it quietly." I said, "Okay, sir. If you are saying so, then it's okay, brother." Okay, brother. So, what should I give, brother? Sir, give an extra force. Which one? Whose value will be how much? Mass of the block into acceleration of the person. They said, "Sir, where should I give it?" They said, "Opposite to the direction of the person's acceleration. Opposite to the direction of the person's acceleration." Where is the person's acceleration? Towards the top, so give it opposite to that, towards the bottom. I said, "Okay, brother." Okay. So, sir, we have given the force here, f = m * a. So, f is the extra force we gave. They said, "Sir, it's given." Now solve the problem. Now, when this person solves it, he will say, "What force is acting upwards?" Sir, Normal. "What is acting downwards?" mg. And a mechanic has added one more force. Which one? Ma. So, Normal becomes equal to mg + maa. Here also, Normal becomes mg + ma. This means your story has become absolutely correct. Now your answer matches. They said, "When did the answer match?" When you added an extra force here. This force itself is called a pseudo force. Is it a real force? No. Is this force actually acting? No. It had to be applied out of compulsion. Okay, sir. Is it a force that acts? No. Is it a false force? Yes. Is it a pseudo force? Yes. Why was it applied? To make Newton's Law of Motion valid. To make Newton's Law of Motion valid inside a non-inertial frame. Why was it applied? To save Newton's Law's honor. Why was it applied? To make Newton's Law applicable inside a non-inertial frame. Okay, if we apply this, then what will happen? Your problems will become absolutely correct. They will stop occurring rapidly. Just like we were facing rapid issues. They will stop occurring rapidly. Are you understanding? So, children often have doubt about when to apply this and when not to apply it. I will finish it in one line. If you are solving the problem standing on the ground, then you don't need to apply the pseudo force. Because there is no need for a pseudo force. You have already solved it here by solving on the ground. So, if you are standing on the ground, you are standing at rest here. See, you are at rest here. Your acceleration becomes zero. So, put zero acceleration there. Put zero acceleration. So, the value of the pseudo force will become zero for you. That's why we don't solve problems standing on the ground. We never apply pseudo force while solving on the ground. Are you understanding? So, in short, I am finishing it in one line: Sir, when should pseudo force be applied? I said, look, if you are solving while sitting on the ground, then absolutely do not apply it. If you are solving while sitting inside the lift, sitting on the bench, then apply the pseudo force. How much? m * a. Now, if they say, "Sir, its velocity is constant." Suppose acceleration is not given. Velocity is constant. Now, if velocity is constant, then acceleration is zero, right? I said, "Yes, so put zero there." End of story. The value of the pseudo force will become zero. Are you understanding? So, this is the thing. If you are solving while sitting on the ground, then you don't need to apply pseudo force. And if you are sitting inside the lift, you are sitting on the wedge. You are sitting inside a car that has acceleration, then before solving the problem, you have to apply pseudo force m * a on the block. Where? Opposite to your acceleration. Now, for example, we did this problem earlier. Now look at this problem. Now, when we were looking at this problem from the ground. Now see this whole story. Now, sir, when we were looking at this problem from the ground, I said, "Yes, sir, we were looking from the ground." So, it appeared to be moving forward. We made the free body diagram. We said, the force acting upwards, the force acting downwards. The force acting forward gave the acceleration. I said, "Okay." Now, suppose, brother, these Lalu brothers, these Iron Man, sat inside it. Does it look like this? Like this. So, how will it appear to him? It will appear stationary to him. And brother, if it appears stationary, then it becomes a problem of equilibrium. But before sitting, what do you have to do? Before sitting, you have to apply a pseudo force m * a backwards. Otherwise, the problem will be wrong. Why? Why do you have to give it backwards? Because the acceleration of this entire system is in the forward direction. So, the acceleration of this person is in the forward direction. So, where will you give the pseudo force? You will give it backwards. They said, "Okay, sir, we will give it backwards." They said, "Now, how to solve the problem?" I said, "Now, brother, solve it." Now there is no problem. Now there is no problem. If I say this is theta, then this will also be, my brother? Sir, this will also be theta. So, sir, now it has become a problem of equilibrium. Now you can solve it however you want. Now you have sat inside, right? Yes, sir, I have sat inside. I have sat inside, so this block appears to be in equilibrium. Does it appear stationary to you? Yes. The force acting upwards equals the force acting downwards. The force acting forward equals the force acting backward. Which force is acting here? T. What is the component of T upwards? T cos theta. T cos theta = mg. Sir, what will go forward? T sin theta. T sin theta = ma. Take the ratio of both. tan theta = a / g. So, a = g tan theta. See, it's the same. See, everything is the same. T sin theta = ma. T sin theta = ma. T cos theta = mg. T cos theta = mg. tan theta = a / g. Everything is the same. Everything is the same, brother. Everything is the same. Everything is the same. The only difference is what? The difference is in the way of saying it. Here you are saying that we are solving it with respect to the ground. Here you are saying that the force acting upwards equals the force acting downwards. T sin theta gave acceleration ma. T sin theta gave acceleration a. Here you are saying that the force acting upwards equals the force acting downwards, and sir, T sin theta canceled out with ma because we are solving from inside. This block appears to be in equilibrium. Are you understanding? Here I am writing. Here it is T, so the component of T will go upwards, T cos theta, and a component of T will go forward, T sin theta. Clear? So, this means can we solve all the problems with pseudo force from the ground frame? Absolutely, we can. You can solve all the problems from the ground frame as well. But there are some problems that become easier when solved with pseudo force. For example, I will take some questions. I will take one question. For example, it's a very standard question. Okay? You will find it everywhere. Okay? That, sir, if I tell you, brother, here is a wedge. Okay, sir. A block, suppose. Okay? Its mass is, let's say, 2m. Here, suppose, is a block of mass m. I said, "Okay?" Its acceleration is in the forward direction, a. Okay? This is, suppose, a, and this is, suppose, b. So, the question is, find the value of a so that block a remains at rest. Such language will be given. With respect to the wedge also, that is, what should be its acceleration so that it remains at rest with respect to it? Are you understanding? Whose acceleration? They said, "Sir, what should be the acceleration of this wedge so that it remains at rest with respect to it?" So, brother, I can solve this question from the ground as well. It's not that I cannot solve it from the ground. What he is trying to say is, tell us what should be its forward acceleration so that it remains at rest with respect to it. This means it is moving. The whole game is like this. The entire, the entire system is moving like this. See how? Now tell me, is the mass going up or down? They said, "It's not going anywhere?" They said, "It's only going forward." It's only going forward. It's only going forward. I said, "Okay, brother." Okay. Okay? So, either you solve it from the ground. I am giving you homework, so solve it from the ground easily. Like we did just now. How? They said, "Sir, see, normal will act here." I said, "Okay, brother, normal will act." "Sir, mg will act downwards." I said, "Okay." The component of normal will go upwards. I said, "Okay, brother." The component that goes upwards, perhaps it will be n cos theta, as far as I can tell. And a component will come forward. I said, "Okay, brother." n sin theta will come forward. So, what will you write? Sir, n cos theta = mg. n sin theta = ma. Your math has become exactly like this, like this, like this, like this math. n cos theta = mg. But normal will come in place of tension. The problem is the same, isn't it? If I remove the rope from this question and make it a wedge like this, it's the same, isn't it? See, if I make this question like this, if I make a wedge like this here and remove everything, then the problem is the same again. Okay, okay, sir. Okay. So, either you do it like this, peacefully. Okay. I will quickly show you once. Okay? That, sir, do one thing. I said, "What?" They said, "Sir, see, sir, normal is acting here." I said, "Move it forward a little." This angle is theta. So, this angle will also be theta. The angle with the vertical will be theta. n cos theta = mg. n sin theta will act forward. = ma. But our intention is not this. Our intention is to learn pseudo force. So, sir, if someone wants to do the same question with pseudo force. They said, "Sir, if I sit here on top of it, will this block appear stationary to me?" They said, "Yes, sir, this block will appear stationary." And if this block appears stationary, then it's a problem of equilibrium. And a problem of equilibrium, my brother, is what? I am shifting it down a bit. Okay? A problem of equilibrium is what? It's easy compared to f = ma. So, what do you have to do? You will say it directly. They said, "Sir, do one thing on this. Apply a pseudo force m * a backwards on it before sitting." I said, "Okay, brother." Sir, this angle is theta. Sir, this angle will also be theta. So, the force acting here will be ma cos theta, and the force acting here will be ma sin theta. Sir, mg is also there. The component of mg will be acting here, mg sin theta. The component of mg will be acting here, mg cos theta. I said, "Okay, brother." And sir, what will be acting here? Normal will be acting. This person sees this block as stationary. Seeing it stationary means the force acting in this direction equals the force acting in that direction. So, you will directly say, "Sir, mg sin theta = ma cos theta." Sir, everything will cancel out from here. a will come out to be g tan theta. Are you understanding? And if they ask for normal, then you can also write normal from here. Normal will be equal to ma sin theta + mg cos theta. This will be your normal. Are you understanding? Clear? So, this is basically the story here, my brother. Okay? So, if possible, memorize the data because the question is very standard. k = gt is a very standard question. In this, like there is a question in HC Verma. There is a question in HC Verma where they have done what? They have kept the same question. Here the mass is 2m. Here they have kept mass m. I said, "Okay." They have tied a rope here and hung a mass m' below. They said, "Brother, tell us what m' will be." So that, so that this a, this b, this c. So that a remains at rest with respect to b. A remains at rest with respect to B. So, what will you say, brother? Let its acceleration be A in this direction. Then the acceleration of this entire system will be A in the forward direction. This is your old question. Pulling force, stopping force, divided by total mass. Okay? So, don't say, "Sir, let's do one thing, let's sit here and apply pseudo force." Yes, you can do that too. But looking from a distance, what should be its acceleration? We have already solved this a little while ago, haven't we? For it to remain at rest with respect to this, what should be its forward acceleration? g tan theta. This is the ground. This is the ground. Brother, this is the ground. Don't consider the ground to be in the air somewhere. Brother, this is the ground. Okay? So, you will directly say, "Oh, sir, tell me, sir. How to write the acceleration, sir?" I said, "Write the acceleration. Pulling force, no stopping force. Divided by total mass, m + 2m + m'." I said, "Okay, sir." Pulling force minus stopping force divided by total mass. Sir, this is the acceleration. Equate it to what? Sir, equate it to g tan theta. We have used the previous result as it is here. Are you understanding? Clear? So, brother, such questions are asked here. Are you understanding? So, do one thing. Write all these things. Then we will do more questions on this. Mistake. Okay? See, I have put the HC Verma question here. You can read this question if you want. It's the same question that I told you just now. Solve it comfortably at home. The answer is also given here. Okay? Okay? Let's move forward on this matter. Now, in the same way, there is another expected question. So, it can come in your exam. That is, brother, suppose here is a parabola, and the parabola is moving forward with acceleration A.

And he said, "Find acceleration." So that the bead remains at rest with respect to the wire. Meaning, there is a bead here, and this green bead, what is it? It is at rest. At rest means at equilibrium. In this question, it is at equilibrium. It should not be called rest, it should be called equilibrium. But with respect to it, always being at rest means being at equilibrium. So he will say, "Tell us, what should be the value of acceleration?" So you will directly say, "Sir, what a simple question, sir." "Sir, if I zoom in." "I said, yes brother, zoom in, sir." "So we will see a small inclined plane like this." "Okay, sir." "So let's assume this angle is theta." You will directly say, "Sir, what does equilibrium mean?" "What should be the value of acceleration?" "It should be g tan theta." Now, what is tan theta? This is a big problem. How to write tan theta? So, you might remember that we study this earlier, that tan theta is equal to the slope, sir? What is tan theta equal to? "It is equal to the slope." Slope means dy / dx, meaning on any curve, if you draw a tangent to any curve, the slope of that tangent tells you tan theta. Which is basically equal to dy / dx. I said, "Okay." "So I will put the value of dy / dx here." "Sir, what will dy / dx be?" "k * 2." Of course, it is obvious that its slope will be negative. "Are you getting it, sir?" "So it will be negative, so x will also be negative." "So let's play with the magnitude, magnitude." "Okay?" "Let's play with the magnitude, magnitude." "So you will directly say that the value of a will be what?" "Sir, a = g * k * 2x." Sometimes, they ask for the location, like they will ask for the location here, like "Tell us what x will be?" "So if I ask for x from here, what will x be?" "a / Sir, a / 2g." "But where will this x go, sir? This x will go in the negative direction." "It will be a negative x coordinate." "Are you understanding?" "Meaning, simply put, a = gt tan theta." "And tan theta is equal to the slope." "Look at the question on this. Look at the question." "The JEE Advanced people asked a question on this." "Once, here it is." "Okay?" "Look at the question carefully." "Okay?" "You might be able to solve the question as soon as you see it now." "What did they say?" "What did they say?" "What did they say?" "They said, 'A piece of wire is bent in the shape of a parabola y = kx²'." "I have made a wire of parabolic shape here." "Bead of mass m on it." "Bead can slide on it on the wire without friction." "They said there is no friction." "It stays at the lowest point of the parabola when the wire is at rest." "This means when the wire was stationary, the bead, our bead, was here." "Okay, brother?" "Okay." "Now wire accelerates parallel to the x-axis with a constant acceleration A." "Now, he did not say where it went." "Did it go forward or backward?" "Okay, fine. We will assume it anywhere." "Let's assume its acceleration." "Let's assume it's forward, given as A." "Okay, brother?" "The distance of the distance is asked." "There is no issue of minus plus." "Of the new equilibrium position." "Ah, the new equilibrium position." "Of the bead where the bead can stay at rest with respect to the wire." "So, it was with respect to the batch earlier." "The block was at rest with respect to the batch." "Now what is it?" "It is at rest with respect to the wire." "So, just pick it up and assume it is the equilibrium position." "You will say, sir, if this is the equilibrium position, then here we can assume a small inclined plane." "The place where the bead is placed will be like a small inclined plane." "So, what should be the value of acceleration?" "It should be g tan theta." "I said, okay, brother." "Sir, what will g tan theta be?" "dy / dx." "And what will dy / dx be?" "Sir, 2kx." "Sorry, what is the differentiation of x²?" "It will be 2x." "So, basically, we should not write 2kx." "We should write it as a * differentiation of x², which will be 2x." "So, what will x be equal to?" "a / Sir, 2gk." "So, a / 2gk, this will be your option B, a JEE Advanced question." "Now you see it yourself." "Can you do it?" "Clear?" "So, remember this result." "a = g tan theta." "I said, okay." "Now, we learned another very good thing from pseudo force." "They said, what?" "They said, sir, if I say there is a lift, a little while ago we saw that the lift is going up with acceleration a, here a mass m is at rest." "You solved it, normal came out to be mg + ma." "You also solved it from the ground frame, and it was also mg + ma." "And you solved it by going inside the lift, and it was also mg + ma." "I said, okay." "But there is one thing we want in this." "Suppose in this case, we sat inside it." "We said, we will sit inside the lift." "Okay?" "This mass is going upwards." "You will say, okay, draw the FBD." "You will say, sir, if you sit inside the lift." "If you draw its FBD." "mg will be acting downwards, normal will be acting upwards." "Because we are sitting inside a non-inertial frame, an accelerated frame." "So, we will have to give a pseudo force m * a downwards." "I said, okay, brother." "Okay." "No problem." "You have given the pseudo force downwards, m * a." "So, if I ask you, what will this person say for normal?" "He will say, brother, normal will be the upward force equal to the downward force." "Can I write it like this?" "m * g + a." "And what can I write g + a as for a while?" "Now, understand carefully." "Normal came out to be mg + ma, which is m common, g + a." "So, if I write g + a as g effective, are you getting it?" "Let me say this, that I sat inside the lift." "Suppose you go into any world, any planet, and you have kept a block m here." "You sit in front of it." "Whatever world, whatever planet, then what will you say?" "You will say, sir, normal will act upwards, mg will act downwards." "So, normal will be equal to mg." "What is the value of g?" "10." "But 10 is for us, right?" "It is for Earth, right?" "If you go to the moon." "If I say this question, put it on the moon." "Okay?" "So, you will say, the value of g there is g / 6." "You will put g / 6 instead of g there." "Maybe you go to some other planet." "You say, we are going to another planet." "We will go to another world." "So, you will write this, right? Upward force equals downward force, normal equals mg." "You will write that, right? Only the mass will remain the same, but the g, this g, its value will be different for different planets, for different worlds." "For our Earth, it is 10." "I said, yes, brother." "So, if I think of the same concept here, I ask you, brother, let's sit inside like this." "Here, brother." "Can I say that in this world of the lift, this block person is sitting here?" "The person is sitting inside." "He can see this block." "He can see this block stationary." "So, what will he say, sir?" "Normal will be equal to mg." "Normal will be equal to what will this person say?" "mg." "I said, yes, brother." "But why can't I say this?" "Sir, in his world, if he wants to say normal equals mg, then can I say that in his world, the value of g has become g effective?" "The value of g has become g effective." "Meaning, he will say the same answer." "He will say normal is mg." "Just instead of g, we will write." "The g of his world." "So, can I say that if you are solving a question in a lift that is going up with acceleration a." "You are solving the question sitting inside the lift." "You are solving the question sitting inside the lift." "You are solving the question sitting inside the lift." "So, either you give a pseudo force with mg." "If the lift is going up, the pseudo force will act downwards." "Either solve it like this." "Or why don't we combine mg and ma in our calculation and directly write g + a as g effective?" "Meaning, sir, if you are going inside the lift, you have entered a world where the value of g is g effective." "You have entered a world where the value of g is g effective." "You have entered a world where the value of g is what, my brother?" "g effective." "Meaning, all your previous questions will be solved." "Sir, if the entire story is wrapped inside a lift, then just replace g with g effective." "Are you getting it?" "Meaning, I want to say this." "Look, if I ask you a question, what will you say for tension?" "You will say, sir, tension will be equal to mg, equal to 100." "Okay?" "Yes, sir." "I put it inside a lift." "And I said the lift is going up with a = 2." "Now tell me, what will be the tension?" "So, you will say, sir, earlier it was mg, it will still be mg." "Oh brother, come on. Earlier it was mg, it will still be mg." "Yes, just instead of g, it's g effective." "Meaning, sir, I sat inside." "Whether you calculate tension from outside or inside, the answer will be the same." "I have combined mg + ma." "Okay?" "So, brother, what is the value?" "Sir, what is the value of m, brother?" "10." "Sir, what is g effective, sir?" "g + a." "Sir, what is it?" "10 + 2 = 120." "Meaning, for this person, the question has become exactly like this." "Exactly like this, as if I hang a block and ask." "I said, tell me, what will be its answer?" "Now tell me, what will be its tension?" "mg." "Just in its world, instead of g, the g in the lift's world, the value of g has now become g + a." "You can understand it like this." "So, catch these two points, my brother." "Which two points?" "If I tell you that there is a lift, suppose it is going up with acceleration a." "Are you getting it?" "Okay?" "So, in its world, the value of g effective will be g + a." "And if a lift is going down with acceleration a, then just put minus instead of a here." "So, your g effective will similarly be g." "Meaning, this is your world." "If you play anything in it, play cricket in it, keep a block, anything." "Are you getting it?" "This is your world." "So, in this world, the value of g will be g + a." "Just like I am picking up some questions." "Look carefully." "If I ask you, brother, suppose, for example, here is m1 and here is m2." "I said, okay." "I ask you, my brother, tell me the tension here, t, what will it be?" "You will say, this t, this t, so this is 2t." "If I ask for t, suppose someone remembers, 2m1 m2 / m1 + m2 * g, this is it." "I said, yes, brother, this is it." "Now, if the question is given like this, that this entire system is going up with acceleration a, then what will you do?" "Sir, you will replace g with g effective, that's it." "This is the tension." "Are you getting it?" "Just this is it." "You can see it with values if you want." "If I say, brother, this is a lift, sir." "This is going up with a = suppose 2." "And we did one thing here." "We hung a 2 kg mass." "We did one thing here." "We hung a 3 kg mass." "We are asked, brother, what is the tension here, t, here the tension is t, so what will be the tension here?" "It will be 2t." "So, if we are asked to tell the value of t, you will write 2." "Sir, m1m2 / m1 + m2 * g effective." "What will you write as g effective?" "Sir, g." "g effective means g + a." "Meaning 12." "So, what I mean is this." "Are you getting it?" "Not only in this question, many questions can be formed in this." "Like one more question, look." "Like, if I ask you, a small question." "I say, this is an inclined plane." "I dropped a block from here." "This angle is theta." "And this length is l." "Okay?" "I said, okay, brother." "This point is suppose a." "This point is suppose b." "I ask you, how much time will it take to move the block from A to B?" "So, you will directly say, S = UT + 1/2 AT²." "I dropped it from here." "I fixed it from here." "So, it will slide down." "I said, okay, brother." "I ask you, tell me, how much time will it take to go from A to B?" "Dropped from here." "So, you will say, sir, apply it this way, sir." "Dropped?" "I said, yes, sir." "What will be its acceleration this way?" "Sir, it will be g sin theta, sir." "So, you will directly say in one line that, sir, we will write, sir, s = s = ut + 1/2." "Acceleration is gsinθ." "ut + 1/2 at²." "Clear?" "So, what will t be from here, my brother?" "Sir, t will come out to be under root of 12 / g sin theta." "I said, okay." "This question is done, a normal question." "Now, if I give this question like this, that we have put it inside a lift like this." "And this lift is going up with acceleration A." "Now tell me, how much time will it take?" "Because time is the same from every frame." "So, you will directly say, sir, the answer will be this." "Just here, where it is g sin theta, sir, instead of g, I will put g + a." "That's it." "That's it." "Your kinematics questions related to the lift will also be done in one line." "Suppose I say this lift is going up." "Its velocity is 20 meters per second." "At this instant, its acceleration is upwards, 2 meters per second." "A coin is dropped from here." "Okay, sir." "And this is suppose a height of 24 meters." "The question will be, tell me, when will this coin fall on the ground, on its floor?" "On the floor, when will it fall?" "You will say, what?" "Okay, sir, let's do the question." "I said, tell me, what?" "They said, sir, sit inside." "I said, I sat inside." "Now tell me, when this coin drops, will you see it coming down?" "I said, yes." "So, for you, has this question become exactly like I dropped a stone from here?" "Yes, sir." "If you drop a stone, if you drop a particle, how much time does it take to go down a height h?" "2h / g." "Just here, for its world, what is the value of g?" "Sir, it's not g, sir?" "It's g + a." "So, your answer will be 2 * 24 / g + a here, which is 12 = 2 seconds." "End of story." "Are you getting it?" "Clear?" "This is how it's done." "Like, if you remember." "We did some questions like this in projectile motion." "We threw a stone this way with 100 meters per second." "You remember." "We threw a stone this way with 100 meters per second at 37°." "Yes, sir." "So, tell me, sir, what was its component this way?" "80." "What was the upward component?" "60." "Okay, sir." "When you threw it this way, it will go, go, go, go, and fall here." "Okay?" "I say, what will be the time of flight?" "6 seconds to go, 6 seconds to come back." "12 seconds time of flight." "I ask you, what will be the range?" "So, 12 * 80." "They say, yes, sir." "Now, if I ask you this question like this." "I say, brother, suppose this is the lift we made here." "Suppose this is a lift." "This lift is going up with acceleration a." "Now tell me, when will it hit the ground of this lift?" "So, you will say, sir, what is the value of g effective here?" "Sir, g + a." "It's going up, so g + a, meaning 12." "So, you will directly say, oh sir, we will sit inside." "We have entered a world where, sir, instead of g, the value of g is 12, not 10." "Now tell me, with what speed did you throw the stone upwards?" "They said, 60." "In 1 second, the velocity will decrease by 12." "You threw it with 60." "So, what will be the time of flight?" "Sir, 5 seconds to go, 5 seconds to come back." "Sir, what will be the range?" "Range?" "The particle will remain in the air for 10 seconds and will move forward at 80." "End of story, the question is done." "Range means the position where it hits the floor of the lift, from here to here." "So, you understand this." "How easy the question became." "As soon as you go inside the lift, just catch this point." "If the entire lift is going up with A, then sit inside the lift." "Okay?" "And then I will say that, brother, you have entered a world where the value of g is g + a." "That's it." "Solve it as if it is the ground." "Just replace g with g + a." "Now, there are quite a few questions in HCB on this." "Now, you can do those." "I will show you." "Look, like this question." "He asked, tell me." "A block was released from here." "So, how much time will it take to go from here to here?" "What will you write, sir?" "Sir, under root." "We just wrote it, 2L / Sir, g effective * sin theta." "The interesting thing is that it is going with constant velocity, so the acceleration becomes zero." "So, the question becomes very easy." "What value will you put for acceleration here?" "Sir, g effective." "So, g effective became g + a." "Acceleration became zero, so the value of g effective became g." "That's it." "This is your simple question, the old one." "Okay?" "You can take a reading of this." "Similarly, look at this question." "Look at this question now." "You can do this." "This is 1.5 kg, 3 kg." "He says, brother, tell me the spring balance system here." "He says, tell me its reading." "Remember, whenever there is a box of this type and a spring balance system is installed inside it, then its sir, assume the tension here is t." "Here the tension is t, so here the tension will be 2t." "So, it gives the reading of this tension." "Now he said, sit inside." "What is the value of g factor?" "One is g, the value of acceleration is 1." "So, what will be the value of g factor?" "It will be 11." "Sit inside, make it g + a." "The question is done." "Okay?" "This is how these types of questions are." "One more question, like." "Like, as you know, there is a simple pendulum." "t = 2π l / g." "There is a formula for the time period of a simple pendulum, which we study in SHM." "Okay, sir." "Now he asked, 'A pendulum of a bob of mass 50 grams is suspended from the ceiling of an elevator'." "Find the tension in the string if he said the elevator is going up with this acceleration." "So, for part A, what will you write?" "Sir, from the time period, this, this is what he is trying to say, brother." "Look, there is a lift, and here we have done this." "A simple pendulum." "Simple pendulum means that simple pendulum, you know, it oscillates like this, like this, with small oscillations." "So, sir, if its acceleration is upwards, a, then tell me, what will be the time period?" "Oh, man, t = 2π l / g, right?" "Yes, l / g." "So, just instead of g, in principle, we write g effective." "That's it." "Either you give a pseudo force and solve it completely, or replace g with g effective." "So, man, the answer will be 2π / g + a, that's it." "Are you getting it?" "Part B." "He said, 'Goes up with deceleration of 1.2 meters per second square'." "It is going up, but with deceleration." "This means the acceleration is downwards." "And if the acceleration is downwards, then what will be the time period?" "2π / g - a." "Why g - a?" "Sit inside, brother." "Sit inside and see." "If you look from the ground, you won't see a simple pendulum." "If you look from the ground, its motion will be like this." "Look, like this." "Oh man, the pen slipped downwards." "Okay?" "Wait." "I will show you with this." "I will show you with this." "Look, if you look from the ground, you will see it like this, look, like this." "Now tell me, what do you see?" "It is going up and oscillating." "But if you sit inside the lift, it will look like this." "So, sitting inside the lift is beneficial, right?" "You see such simple motion, you see like this." "Are you getting it?" "So, sit inside." "Now, wherever you see g, put g effective there." "After that, he further said, sir, 'Goes up with uniform velocity'." "So, uniform velocity means acceleration is zero." "So, t will come out to be 2π L / t." "By the way, you can skip this question if you want." "Okay?" "Because we will do this question again." "When we study simple harmonic motion, we will see this question again." "So, this was my brother, the concept of G effective, and this was our concept of pseudo force." "If any child wants to note this, son, they can note it." "Pause the screen and note down the useful things behind it." "Just write this line." "Write, if a lift is going up with acceleration A." "And if I solve the question sitting inside the lift, then inside the lift, assume that the value of g has become g effective = g + a." "Write this line." "Clear?" "Some children will say repeat." "Go back, go back." "Go back 10 seconds and repeat." "Man, listen to it yourself calmly." "Okay?" "Write it down." "Okay, brother, now let's move to the next part, which is called constraint." "Basically, today, basically, you can think of it like this, the probability of it appearing in the exam is very low." "Okay?" "But it is a small concept." "If you look at it once, it will be very beneficial." "What if by chance a question appears in the exam, then you will be able to do it." "So, I will start it." "Suppose a situation is in front of you like this." "What?" "You can think of it like this, for example, if I tell you." "This is an inclined plane." "This is the ground." "I said, okay, brother." "Okay." "And the first question I took like this, I put a rod here like this." "And here I put, my brother, a stopper like this." "I said, okay, brother." "If you leave it to its own fate, then perhaps you will feel from this that sir, there will be a force on it, mg sin theta, which is trying to bring it here." "There is no friction or anything here." "It is free to move." "Okay, sir." "So, you must feel that this rod is applying a normal force on this wedge towards this side." "Both are trying, aren't they?" "Both are touching, so a normal force is acting." "I said, absolutely correct." "So, if I make the FBD of this wedge, will there be a normal acting on it like this?" "I said, yes, brother, a normal will act like this." "So, will a component of this normal go forward?" "Will a component go down?" "I said, absolutely correct." "It will go forward, it will go down." "So, the downward component will be balanced by the normal from the ground, mg, with mg and others." "But the normal in this direction, will it push the wedge forward?" "Will it apply a force forward?" "Will it accelerate forward?" "They said, yes, sir." "So, these are the types of questions." "We have given this situation in front of you." "And we said, my brother, tell me, what should be the relation between a1 and a2?" "We have put a stopper here, so it can only move this way." "And it wants to move this way." "This brother is moving forward." "Its acceleration is a1 this way." "Its acceleration is a2 this way." "So, tell me, what is the relation between a1 and a2?" "Or if I give the value of theta as 37." "If I give the value of a1 as five." "Then tell me, what will be the value of a2?" "So, these types of questions are seen in wedge constraints." "So, what does wedge constraint say?" "Okay, sir, what does it say?" "I said, brother, wedge constraint means, simply put." "Let's get to the point directly." "Okay?" "That, sir, if I talk about." "Sir, the common normal between these two bodies." "I said, yes, brother." "Sir, there will be no relative motion along the common normal." "Are you getting what I mean?" "What I mean is that there will be no relative motion along the common normal." "This means that the magnitude of the acceleration of both bodies along the common normal will be the same." "Clear?" "Or, the acceleration of both bodies along the common normal will be the same, my brother." "Now you will think, sir, why is this happening?" "We will see the reason for this later." "You will read it in Work Power Energy." "We will see in Work Power Energy that, brother, the net work done by the common normal is zero." "There are two or three reasons for this." "The first reason, which I am telling you, is that the net work done by the common normal is zero." "You can see this from there as well." "But for now, catch it as a property." "They said, sir, what?" "They said, what does the wedge question say?" "I said, the wedge question says that the components of acceleration along the common normal are the same." "You can understand this by another method." "They said, sir, can the acceleration of the person behind be greater?" "If the acceleration of the person behind is greater, then it will penetrate into this, won't it?" "It will penetrate into this." "It cannot happen like that." "Okay?" "They said, yes, sir, you are also saying this correctly." "And sir, if its acceleration is greater in this direction, then it will remain in the air, so then how did its acceleration become a2?" "Meaning, you understand." "So, you can explain it exactly like the constraint of a rope." "But ultimately, the result in front of you is this, that you catch this point." "Along the common normal, there will be no relative motion." "So, we will say that the acceleration of the people along the common normal will be the same." "So, just remember one line for doing wedge constraint questions." "They said, first find the common normal, and break down the acceleration of the bodies along the common normal, and equate them." "That's it." "If you want, you can write the points." "What?" "They said, first find the common normal, and break down the acceleration of the bodies, meaning, meaning the acceleration of the block, along the common normal, and equate them." "For example, if I ask you in this question." "I said, tell me, what will be the relation between a1 and a2?" "Sir, this angle is theta, so this will also be theta." "I said, okay." "So, sir, this angle will be 90 - theta." "I said, okay." "So, sir, sir, what will be the component of its acceleration along the common normal?" "What will be the component of a1 this way, my brother?" "You will directly write, sir, it will be a1 cos 90 - theta this way." "Okay, sir." "What will this be equal to, sir?" "This body, this body, along the common normal axis, with what is it going?" "It is going with a2." "That's it." "a2 = a1 sin theta." "Are you getting it?" "And look at the question, and look at more questions." "And look, and look, and look, and look, and look, and look, and look." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." 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"Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." "Like, like, like, like, like." 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Yes. So push these onto it normally, then this gentleman is going backward. So what is the relation between a1 and a2? What would you say, sir? First, do one thing. Find the common normal. I said, find it, brother. Common normal, if you find it, the common normal means what we used to make the free body diagram, sir, this is the common normal. Any problem? They said no problem. Okay, sir, no problem. I said, okay. Now what do you do? They said, sir, now do one thing, sir. Break both accelerations and equate them to the common normal. So look carefully, sir, this is a1 here. So can I say this? I'm shifting this vector up a bit. Sir, the acceleration of this person, the acceleration of the person below, the acceleration of the yellow person below is a1. Its acceleration below is a2. I'm picking this up and putting it here. So you will directly say that its acceleration below is a2. Are you understanding? These are the acceleration vectors of both people. Now what do I have to do? Break them and equate them towards the common normal. Sir, if this is theta, then this will also be theta, so this will also be theta, and this will be 90 - theta. So tell me here, in this question, tell me what? They said, sir, if its acceleration is a1 here, then what will be its component here? Towards the common normal, what will it be, sir? a1 cos 90 - theta. Okay, sir. Sir, the acceleration of this red body is a2 downwards. It's a2 downwards. I've shifted this vector downwards. What will be its component here, sir? a2 cos theta. These two will become equal to each other. You will write it directly from here. Sir, what will this be, sir? If a1 sin theta, then it means a1 tan theta = a. Are you understanding? Is it clear? Okay, brother? Okay. Let's take another question on this. Let's take another question on this. Like this question is here. If possible, try it, all students, in your rough copy. Try it right now. Tell the angle between a1 and a2. Quickly. This angle is theta. Quickly. Come on, sir. How will we do it? I said, brother, find the common normal. Sir, here is the common normal. Okay, sir. After this, I said, here is the common normal. After that, I will speak directly. They said, sir, make its free body diagram here, brother. Assume this acceleration is a2 here. Shift it a little to the right. Shift A2 up so that it's easy to take the angle from here. I said, okay. And what is its acceleration below? a1. Shift this down, my brother. This is your acceleration downwards. How much? a1. Now say, sir, this angle is theta, so this angle will also be theta. So this angle will become theta again. So how will you write it? Sir, what will be the component of a1 here? You will directly write a1 cos theta. And sir, what will be the component of a2 here? They said, sir, this angle is 90 - theta, so you will write a2 cos 90 - theta. Make these two equal. a1 cos theta = a2 sin theta. And let me tell you one thing, if both accelerations are perpendicular to each other, like a1 is downwards and a2 is to the right, then catch this thing that if the component of a1 in this direction has cos, then its sin will come. The component of a1 towards the common normal has come as cos, so a2 will have sin in this direction, not cos. Because they are perpendicular to each other. If this angle is theta, then that angle will be 90 - theta. Okay? So if cos theta remains cos theta, then cos 90 - theta will become sin theta. So you can do it quickly too. They said, how can we do it quickly? I said, quickly you can do all these questions again. Like this question was. This question was. If you want to do it quickly. So how will you say it? Sir, look, do one thing. I said what? Sir, what is its acceleration downwards? a2. So what will be the component of a2 here? a2 cos theta. Just like mg is downwards, mg is there, so the component of mg will be mg cos theta, mg sin theta. So brother, a2 is downwards, so what will be its component here? a2 cos theta. Make it equal to sir a1. Sir, these two, sir, these two are perpendicular, so sin will come for this. That's it. Are you understanding? You can do it this way too. You can do it this way too. Like this question is done. This question is done. Now how will this be done, sir? Look, what is downwards? a1. So what will be its component perpendicular to the incline? Sir, it will be sir a1 sin theta. So equal to sir a2 with cos theta. So one has sin, sin theta. So see, it's going the same way. It's going the same way. It's going the same way. It's going the same way. Hey, it's not going the same way. Sorry, I wrote it wrong here, brother. Oh, mistake, brother. a1 sin theta is not there. Okay? If I had placed a block here. mg acts downwards, so what will be its component here? mg cos theta. And what will go here? mg sin theta. I'm saying this point. mg is downwards, right? So mg cos theta goes here. Similarly, who is downwards? a1. So the component of a1 here. And towards the common normal, what will it be? a1 cos theta. So you will directly write a1 cos theta = a2 sin theta. That's it. Okay? So this is, my brother, your batch constraint. Note down all these three questions in your copy. Okay? Believe me, if by chance a question comes, it should come from here only. Although the probability of it coming is very low. Note it down, student. Come on, brother, now let's move to our next part, which is called the Virtual Work Method. It's a very lovely method. Okay? With this, your many pulley-pulley type questions will be solved in a single line, in a snap. In a very good way. Please attend the lecture. Okay? It won't be very long. We will give it only 15 to 20 minutes, and in 15 to 20 minutes, we will solve at least 15 to 20 questions. And believe me, if you connect it once, if you understand it well once, then no matter where the question is from, from any book, from any exam, you will definitely do the questions with a smile. Okay? Let's see, brother, what is the Virtual Work Method. I said, look, brother, there's just one condition. I will tell you this thing, don't go into the reason for it, because we will study the reason in Work Power Energy. Okay? So for the next 5, 10, 5, 4, 5 minutes, it might be a little difficult for you to understand. Okay? So be patient. Okay? Be patient. They said, what is the Virtual Work Method? I said, brother, look, suppose I say this, brother, there is a block here. Okay, sir, there is a block here. Here I have tied a pulley like this. Okay, sir. And here, brother, I have placed another block like this. Like this. Okay, sir. Okay. I have given this whole setup as a system. I said, okay. Okay. So if I say this, brother, its acceleration is A1 forward. Its acceleration in this direction is A2. These gentlemen will go forward. These gentlemen will go forward, so they will go downwards. Okay. Okay, sir. Okay. So what does the Virtual Work Method say? I won't go into much detail about it because most of it will go over your head, and you don't need to understand most of it. Okay? We will study its reason in Work Power Energy when the Work Power Energy chapter comes. For now, I will still give the reason, which is that in Work Power Energy, we will see that the net work done by tension is zero. Okay? The net work done by tension is zero, my brother. What is work done, sir? Work done is f.d, perhaps someone has read the formula. Okay? So if I talk about this, then brother, assume tension is acting forward on this. I said, okay, brother. Tension is acting upwards on this. I said, okay, brother. Tension must be acting on this in this direction. I said, okay, brother. Assume the tension on this is t1. Assume the tension on this is t2, and assume the tension on this is t3. We know t1 and t2 are equal. We know we will equate them later. Okay? So the Virtual Work Method says that the net work done by tension, meaning t1.x1 + t2.x2 + t3.x3 + t3.x3, is equal to zero, my brother. Sir, what are x1, x, x3? I said, look, work done is f. displacement. Assume this person moved x1, this person moved x2 backward, this person moved x3 downwards. Okay, sir? So the tension acting on all the blocks, the individual tension, what am I doing? I'm calculating the work done by tension on this. How much will it be? I'm calculating the work done by tension on this block. How much will it be? I'm calculating the work done by tension on this. So when I add the net work done, it comes out to be zero, brother. Now, the advantage we get from this is that if I differentiate this, then brother, the differentiation of x1 is my brother, v1. The differentiation of x2 is my brother, v2. The differentiation of x3 is my brother, what will it be? My brother, v3. I said, okay. What will this be? They said, sir, this will be zero. If I differentiate it one more time, then this will become t1.a1 + t2.a2 + t3.a3. This will become equal with the proper vector sign. I know it might seem a little strange to you. But but now you start from here. I want to tell you one more thing, that if I say what is a.b? Then you all know, sir, a.b is ab cos theta. If I say that the value of theta, my brother, is 0 degrees, suppose, meaning there are two vectors whose dot product we want to find, both are parallel. Okay, both are in the same direction. So cos theta, the value of theta is zero, but ab will become what? Sir, ab will come. This means it will be +ab. Okay? And if I say that if the value of theta is 180 degrees, then cos 180 will be -1, so this will become -ab. -a * b. I said, okay. Now I want to use this here. So look carefully, what will I write here? They said, sir, we will write here what, what, what, what? They said, sir, if suppose I apply this here, then look carefully, my statement will be sir t1aa1. I am using this statement. t1a1 + t2a2 + t3aa3. It's that easy, look carefully. Equal to zero. It will become even easier after a while. Okay, sir? So I said, what does this mean? It means, my brother, look carefully. They said, sir, where is the tension on this? Forward. Where is the acceleration on this? Forward. Is the angle between them 0 degrees? Yes, sir. Is it also true that if there are two vectors and the angle between them is 0 degrees, then the dot product is what? a * b. So this means I can write t1.A1 as what? Sir, t1 * a1. Look, I'm saying this. Same direction, right? Same direction. Okay? Same direction, right? So just multiply. Now, for example, talk about this. Don't look whether it's forward or backward. Just see if the direction is the same. Look, tension is backward. Acceleration is backward. The direction is the same. So it means + t2 * a2. Or you can write it properly. t2 * a2 * cos 0. Or you can write it like this. For this, sir, t3 is upwards and a3 is downwards. I said, okay, brother. t3 is upwards, a3 is downwards. So what sign will I use here? Minus. t3 upwards, a3 downwards. Both signs are opposite. This means you will directly write - t3 * a3 = 0. First, learn to apply this. First, learn plus and minus. See, either you write it like this. Okay? t1 a1 cos 0. Here, what is theta1? What is the value of theta here? 0 degrees. Here also, the value of theta is 0 degrees. Here, the value of theta is 180 degrees. Sir, how is this zero? Where is the tension? Forward. Where is the acceleration? Forward. So the angle between them is 0 degrees. Where is the tension? Backward. Where is the acceleration? Backward. So the angle between them is 0 degrees. Where is the tension? Upward. Where is the acceleration? Downward. So the value of theta is 180 degrees. Either you solve it like this. Sir, ta cos 0 + t, sorry, t1 a1 cos 0. t2 a2 cos 0. t3 cos 180. Or I would say, let's just know this thing. Now we also need to save some time. So we will just do one thing. Sir, multiply the tension with the acceleration. That's it. Okay? If the direction is the same, we will put a plus sign. And if the direction is opposite, we will put a minus sign. Direction is the same. Okay? So plus, and if the direction is opposite, then minus. That's it. Understood? Just do this. Now after this, after this, you apply the previous things. You know this, sir, t1 and t2 will be equal. So now I am removing this, brother. I said, if this tension is t, then this will also be tension? They said, this will also be tension t. So what will this tension be? Oh, sir, this tension will be 2t. Okay? Or I will do one thing. I will write it in this itself. Okay? If I say this, my brother, if this tension is t, then the rope is the same, so the tension is the same. t2 will also be t. t. So this will become 2t. Now I am putting the value here. Tension is here. Acceleration is here. So what will you write? t * a1. Here, where is the tension? Backward. Where is the acceleration? Where will you write? Sir, t * a2. I said, okay, brother? What will you write for this? So - 2t * a3 = 0. Here, t is taken out as common and gone. a1 + a2 = 2 * a3. This relation has come out. Now I ask you a question. I said, brother, its acceleration is four. Its acceleration is three. So tell me, what will its acceleration be? You can find it by putting the value here. I hope you have understood it reasonably well. But you will understand it even better when I show you the questions and make you do the questions. So now look at the questions. Okay? The questions will be very smooth, like butter. If I ask you, its acceleration is four downwards, then tell me what its acceleration will be upwards. Oh man, we already know this. If it goes four downwards, it will go four upwards. Okay? But no, we want to do it properly. Okay, sir. Assume the tension here is t. t. I said, okay, brother. Okay. Now what do you do, sir? Tension is upwards, acceleration is upwards. So what will you write? t * a2. Sir, tension is upwards, acceleration is downwards. So - t * a1. What is a1, brother? Four. Directly equal to zero. t is taken out as common. What will a2 come out to be? Four. Understood? Is it clear? Okay, sir, it's clear? Moving on. Let's talk about this. Sir, assume the tension here is T. t. This T, so this is 2t. Okay? Okay. Come on, sir. Let's talk about this. Let's talk about this. What will you write? Sir, t * a2. He asked, tell me this acceleration. Yes, we will tell you. No problem. This is a block. 2t upwards, acceleration downwards. - 2t. What is the acceleration? Six. Equal to zero. So this means t will be taken out as common. So what will be the value of a2, brother? 12. This means its acceleration will come out to be 12. The thought might be coming to your mind, sir, the mass is not given. Yes, absolutely, the mass is not given. Oh, sir, the mass is not given. Then how is the question happening? I said, this is what we have to study. This is the constraint of the rope, this is the beautiful article. It doesn't matter about the mass, brother. Here, we just have the mass, whatever it is, it doesn't matter. Yes, the mass can be asked after this. Are you understanding? I can tell you, look, I'll do one question here. I'll give you an idea. I can tell you, brother, if its mass is 10 kg, then tell me what its mass will be. Okay? Then you will say, sir, make its free body diagram. Sir, the force upwards is t. Minus the force downwards is t - 100 = 10 * a. Have you found its acceleration? Yes, you have found its acceleration. You know its acceleration. Its mass is 10 kg. So what will be acting downwards? 100. What is acting upwards? Tension. So can you find this tension? They said, yes, you can find the tension. If this tension is found, then make its free body diagram. What is acting upwards? 2t. Do you know this force? Yes, brother, you know it. Assume its mass is m. mg will be acting downwards. What equation will you write? mg - 2t = its mass * its acceleration. That's it. One equation will solve for the mass. Okay? But well, we don't have time for this right now. We are not focusing on this. We are focusing on what? Constrained motion. How are we writing the equation of constrained motion? How are we doing this t.? Like look at the next question. Like I have given this one here. It might look a little strange to you here. Okay? Okay? You might be scared looking at it. But look here, if I ask you, brother, tell me its acceleration. Tell me its acceleration. So look, assume the tension here is t. t. Okay, sir. Now, this t, so this is 2t. Okay, guru ji. Tell me, what will you write? For this, I will write t * a1. What is the value of a1? Six. Both are going in the same direction, so plus sign. For this, 2t upwards and this downwards, so - 2t * 4. Plus t backward. a3 backward. t * a3 = 0. As soon as I solve it, t will be taken out as common. So a3 will come out to be 8 - 6 = 2. In such questions, remember, if by any chance you calculate the acceleration and the acceleration comes out negative, then don't think your question is wrong. Then understand that brother, the acceleration is negative, which means the direction we assumed is the opposite direction. Understood? That's it. Well, moving on. If I ask here, I said, brother, tell me, what will be its acceleration? So listen to the method for this. Is it going this way or this way? We don't know. Will it go up or down? Suppose in some question, someone doesn't see whether it's going up or down. Then I will say, brother, do nothing. Assume wherever your heart desires. And this is my suggestion. Assume it upwards. Assume it upwards. It is A1. This is A2. Assume its acceleration is upwards. If I assumed correctly, my answer will come in positive. And if I assumed the direction incorrectly, my answer will come in negative. But my question will never be wrong. I will speak directly. I said, come on, brother, make the free body diagram. Brother said, sir, assume the tension in the rope is t. t. So what will be the tension here, brother? t. This t, this t, so what will be the tension here? 2t. So you will directly say. Sir, what will you write for this? Sir, the acceleration has also come. The tension has also come. t * a2. Assume it upwards. Yes. Assumed upwards. Assumed acceleration upwards. Tension is also upwards. 2t * a2. For this, t is upwards, a3 is downwards. So - t * 8 = 0. So from here, what will you write? They said, sir, this is 2t. t is taken out as common. So sir, from here you will write what? They said, sir, 2t. 2 * a2 will come out to be, my brother, six. This means a2 will come out to be six. Oh, a2 has come out positive. This means the direction we assumed is the same. Okay? So look at more questions. Like this question. You try it. Try the question. Pause the screen and try it now. Write in one line without a rough copy. Solve it in one line. Done. Look, sir, what to do? I said, brother, what to do? Assume tension t at some place. I assume the tension here is t. tt. tt. This will also be t. tt. This will become 2t. This will become 2t. I said, okay. Let's start. Where is the tension? Upwards. Where is a3? I said, assume it upwards. So what will you write? 2t * a3. Plus, t is upwards. a2 is downwards, brother. Oh ho, so minus sign will be used. Look, pay close attention to the sign. Pay attention to the arrow. The arrow is downwards. Okay? So minus sign will come here because the tension is upwards. Tension and acceleration are opposite. t multiplied by its acceleration is what? Eight. Both are upwards. + t * 4 = 0. If I ask for a3 here, sir, t will be taken out as common and will come out. So sir, this was eight. Eight minus four is four. Four divided by two will come out to be sir, two. Done. Look how easy it is. Okay, many children get scared looking at it. Okay. Assume the tension here is t. Okay. t. This t, this t, so this will be 2t. Now look. They said, what will be the acceleration upwards? t * a2. Okay? Plus, sir, 2t. Three t upwards, acceleration downwards. Six. So - 3t * 6 = 0. So what will a2 come out to be? 6 * 3 = 18. That's it. Okay? And look, and look, and look, and look, and look, and look. Like this question. Okay? I will say, brother, assume the tension here is t. So what will you write? t. Rope is the same, so tension is the same. In such questions, rope is the same, so tension is the same. Sir, here also t. Here also t. Here also t. Here also t. I said, okay. Sir, this t, so this is 2t. Sir, this, sir, this t, so this is 2t. I said, okay. Let's start the question. Sir, what will be its acceleration? Upwards or downwards? Oh, brother, assume it's upwards. You will be at peace. Always assume it upwards, and the calculation will be quite easy. If you assume incorrectly, it will come negative. But the answer will not be wrong. I will say it directly. I said, come on, brother. Assume it upwards. So what will you write? t * 4. Now listen, sir, don't listen. Okay? t * 4. Sir, what were you saying? I will tell you after a while. No. Okay, okay, sir. What is upwards, sir? Sir, 2t is upwards, and what is the acceleration? a3. Sir, here, here, what is it? + t * a2. What is a2? Six. Equal to zero. If you look, t is taken out as common. So a3 will come out to be 8 / 3. What was assumed is absolutely correct. Moving on. Similarly, it might be placed on an inclined plane. So there is no need to be afraid. Whether you place it on an inclined plane or in any other way. The question will be solved like this, brother. They said, what? They said, brother, assume the tension here is t. So this is t. This t, this t, so this will be 2t. So this will be your 2t. You will write it directly. Sir, for this, 2t * a2. For this, t is upwards, acceleration is downwards. - t * a1. And what is the value of a1, my brother? Four. Equal to. Yes, equal to zero. This will be 4/2. So what will a2 come out to be? Two. Moving on, sir, to this. I said, assume the tension here is t. t. So here also the tension is t. This t, this t, so the tension here will be 2t. a3, we don't know where it's going. Assume it upwards. You will be at peace. Always assuming it upwards will make the calculation quite easy. If you assume incorrectly, it will come negative. But the answer will not be wrong. So t * 4. Now listen, sir, don't listen. Okay? t * 4. Sir, what were you saying? I will tell you after a while. No. Okay, okay, sir. What is upwards, sir? Sir, 2t is upwards, and what is the acceleration? a3. Sir, here, here, what is it? + t * a2. What is a2? Six. Equal to zero. If you look, t is taken out as common. So a3 will come out to be -5. This means it was assumed upwards, and the answer came negative, which means the acceleration will be downwards. So a3 will be five downwards. Okay, okay, sir. You were about to say something, brother. I wanted to say this, look, in every question, t is taken out as common and gets canceled. So if possible, move one step ahead. Try to move one step ahead of other students. Try to develop your vision. If such a question appears, if your calculation is fast, then cancel t. That's it. Take t out as common from the beginning. Like, look at the next question. Like I, sorry, we will see this later. Okay? No, brother, leave it. Okay? What if you make a mistake in a silly mistake? I will explain it in this itself. Okay? I will explain it in this itself, brother. Okay? Look, assume. If I want to tell you that whenever you see such a multi-type question, you can go directly if you want. Look, try to go directly like this. Like this. How? Sir, where is 2t? Upwards. Where is a2? Upwards. So t will be taken out as common and will be gone, right? Yes. t is removed. What is left? Two. 2 * a2. Plus, where is this t? Upwards. Where is the acceleration? Downwards. Okay? t * a1. Remove t. Directly a1 = 0. a2 = 2. I mean to say, look, meaning t will be taken out as common, right? If you are scared, then brother, write the statement. I mean to say, if you are scared, then do it like this. There is no problem. But if you want to save some time, then you can write it like this. Look, t * a1. t is gone. So what is left? Sir, 1 * 4. Talk about this. 2t * a3. Okay? 2t is gone. * a3. Plus, sir, t * a6. t is taken out as common. Equal to c. So look, from here, you can write the answer in one line. Are you understanding? Okay? Otherwise, brother, no problem. Do it peacefully. Now look at this question. Children get scared looking at these questions. Oh, it's very easy. They said, how? I said, brother, tell me one thing. Tell me, where will the tension be acting on this? Sir, it will be acting here. Where is its acceleration? Forward. Where will the tension be acting on this? It will be acting backward. Now tell me, what will you write for this? Sir, t. Sir, we used to write dot products, right? t.a, right? Check it here. The statement I started with, I started from here. Sir, t.a. We were writing the dot product of tension and acceleration. I said, yes, brother. We were writing tension and acceleration together. So what will we do, sir? t. Sir, acceleration has come. What is the angle between them? 37 degrees. So what will you write, sir? a.b = ab cos theta. Okay, sir? Acceleration has come here. Tension is backward. The angle is 180 degrees. So you will write this directly as t * a1. Minus sign, equal to zero. t is taken out as common. a2 * cos 37 is 4 / 5 = a1. And what is the value of a1, brother? 10. So this means a2 will come out to be 50 / 4. And yes, the same result for velocity. The same result for velocity. Sir, because now we are playing with this. Okay? If he gives a question on this. Then the same result for velocity. Sir, what do you mean by this? I said, what I mean is, suppose in some question, he has given velocities here at some time. He said, brother, tell me what its velocity will be. Tell me what v2 will be. If its velocity is, suppose, six downwards. Then you will solve it in the same way. How, sir? t * v2. And for this, - 3t * 6 = 0. So v2 will come out to be 18. You will solve it in the same pattern. Okay? All right, sir. Okay. Okay. Oh, this is very interesting, sir. Very interesting. Very easy. I said, yes, very easy. Come on, let's talk about this. Sir, if we talk about this.

Look at the tension. On what should the tension be observed? On the block. On the masses. On the masses. Do not look at the pulley. Okay? Because the pulley is ideal and the pulley is massless. We only need to observe it on the mass. Okay sir. Sir, make its free body diagram. What tension will be acting on it from this side? Tension t. So, tension will be acting upwards on it, t. Sir, the tension is this way, the acceleration is forward. So what will we write? t * a2. Sir, here cos 37 will come. I said okay, tension upwards, acceleration downwards, - t * a1 = 0. So a2 * cos 37 is 4/5 = t common factor came out, equal to a1. a1's value is eight, so a2 will come out to be 10. Okay, okay. Similarly, this is also a standard question, sir, you can do this too. Sir, tension will be acting on this side, t, and tension will be acting on this side, sir, t. So what will you write, sir? Tension this way, a1 this way, so what will you write? t a1 cos theta + sir, tell me about this. I said, for this, draw two lines so that you can see it more comfortably. Sir, its acceleration is A2, its acceleration is here. I said okay. So sir, you see, if this angle is theta, then this angle will also be theta. Okay? If this is θ2, then this will also be θ2. Where is the acceleration? Forward. Where is the tension? This way. What is the angle between them? So you will say, sir, the angle between them will be 180 - θ2. So what will you write here? T * sir a.b = ab cos 180 - θ2 = 0. From here, a1 cos θ1 will come out. If this is θ1, then it will be equal to a2 cos θ2. Sir, how did this come? cos 180 - theta is - cos theta. Here, instead of plus, it will become minus, and going there, it will become plus. Tell me, did you understand? Is it clear? Okay, sir. Let's move forward. After this, suppose a question is this, do this quickly. Pause the screen, do it quickly. Let's go. Sir, let the tension be t. tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt 2t in one line, t * a2 2. Okay, brother. For this, 2t upwards, acceleration downwards, - 2t * 8 = 0. a2 will come out to be 16. Next, see more questions. Like this type of question. No problem, brother, we can do such questions. So look, brother, here let the tension be tt, 2t, 2t, 2t, 2t, 2t, 2t. Now look carefully. This 2t, this 2t, so this is 40, 40, 40, 40. So write this 40 first for the block. For the block, tension upwards, acceleration upwards. Then write for the platform, 40, 2t, 60, and 70, 70 upwards, and acceleration downwards. Acceleration is seven. Equals 0. a2 will come out to be 49. Some children think, sir, this is seven, this is seven. 7 / 7 = 1. Don't make such mistakes. That's why I'm saying, if you have even a little doubt, put the values calmly and solve calmly to get the answer. Anyway, let's move forward. Now questions of this type you will see in your sheets. Now brother, suppose, sir, make its free body diagram. What is acting behind? Tension t. Let the tension in this rope be t. So look, t. Okay, sir. So here tension t, here tension t, so tension will come this way, 2t. Sir, here tension is t. Here tension is t. So tension will come this way, 2t. Sir, here t, here t, so tension will come behind, 2t. So what will be the tension on this block? 2t, 2t, 4t. Acceleration forward is a2. Minus, sir, what will be the tension behind this block? Sir, t behind and 2t behind, so 3t tension is behind. And its acceleration is forward. Tension is behind, acceleration is forward, that's why minus has come. What will you write? 3t * 8 = 0. So a2 will come out to be six. Did you understand? Do it quickly. Sir, sir, let the tension on this be t. Okay? This t, so this t, this t, this t. Rope is the same, so tension is the same in these questions. tt. So this 2t. Here also 2t will come. Here also 2t will come. Sir, this t, this t, so this will be 2t. Sir, this t, this t, so this will be 2t. Okay? What will you write? 2t, 2t, 2t, 6t. So 6t * a2. 2t, 2t, 4t. And this 5t. 5t multiplied by acceleration is 8. Equals 0. Is it clear? This will come out to be 40 / 6. a2 will come out to be 40/6, my brother. So, brother, these questions are done like this. Now do this question quickly. Look. Look, many pulleys etc. are given. No problem, brother. If given, then where to start, brother? Start from where t becomes 2t. Okay? So I feel it's beneficial to assume t here. Okay? This t, so this t. This 2t. This 2t. This 40, 40, 40, 40, 40. This 40, this 40, 40. So this is 80, right? The upper one, we will do the lower one. This is also 40, this 40, 40. So this is 80. Now look carefully. Look, this 8T, this 8t, so this is 16t. This 16t. So tension will be acting backwards on it, 16t. It has given velocity instead of acceleration. So no problem, no problem. I said the result is the same, the statement is the same. So what will you write for this? Sir, tension upwards and velocity upwards. 8t * 8. Sir, tension upwards, velocity downwards. 2. Minus t * 2. Let's finish this. Catch this. 2t upwards, two upwards. 2t * 2. I said okay, brother. Move forward, move forward, move forward, move forward. Come to this. Sir, its acceleration is downwards. Sir, its velocity is downwards, tension is upwards. - AT * 1. I said okay, brother. Talk about this. Sir, it has asked for the velocity of E. Where to assume it? Let's assume upwards. What will you write? 4T * V. I said, okay, brother. Its work is also finished. Now talk about this. Sir, it is 16 tension in the backward direction and velocity is in the forward direction. 4 = 0. Finished. It's a long statement, I admit, but it's a solvable question. It's not like you can't do it. Okay? This is a question from our PW JEE module. You might find this question there. Okay? So whatever it is, I think now you can do all such questions. So brother, tell me right now in the comment box below by typing, yes sir, we can do it. Quickly, pause the screen now. If everything is understood, then write, say yes sir, we can do constrained motion well now. Is it clear? Okay, let's move forward. Now it's done. Okay. Now let's go to the next part, which we call acceleration questions. Meaning, sir, you are given many pulleys and masses, and you have to find out, brother, tell me what is the acceleration of each mass. Okay? With a lot of patience, first look at one or two questions, how I am solving them. Then I will tell you a way to do those questions even better. And after that, whether you have 10 masses, 20 masses, 50 masses, five pulleys, or 10 pulleys, you will be able to do all the questions. Okay? Look carefully. Okay, sir. Suppose I took a small question like this, find the acceleration of each mass. Tell me. I said, first I will tell you a normal method that you will find everywhere in books. That's the approach most children take first. So you see this method too. What do they say? They say, sir, this is four mass m, this is five, this is this 4 mm, this is m. This looks heavy. This means it will slide downwards. It will go downwards. So let's assume, brother, its acceleration is downwards, a1, and let's assume, brother, its acceleration is upwards, a2. Sir, make its FBD. I said, make it, brother. Sir, tension will be acting on it, t. I said, okay, brother. So this tension will be 2t. So this tension will be 2t. What will be acting downwards, my brother? Mass mg. And what will be acting downwards, my brother? 4mg. I said, okay, brother. Okay. Now if I talk about, sir, make its FBD. So downwards you will say, sir, 4mg - tension = 4m * a1. I said, okay, brother. Okay. Next, sir, make its FBD. Sir, what is the tension acting upwards? 2t - mg. I said, okay, brother. Equals m * a2. Okay. These are two equations. I said, okay. And the third, sir, is our constraint motion equation. For this, we will write, sir, 2t * a2. For this, we will write -t * a1. We just saw that. - t * a1 = 0. This means 2a2 will come out to be equal to a1. This is your first equation, and this is your two equations. So look, the story is that how many variables do we have? Brother, we have three variables. Which ones? Sir, we don't know a1, we don't know a2, we don't know t. So we need three equations. So you can think of it like this, brother, we have written these two equations for the individual masses. We made its FBD. We wrote its equation. We made its FBD. We assumed its acceleration downwards. We wrote its equation. Now two equations won't work. Our two equations won't work. We have three variables, so we need three equations. So how will the third equation come? They will say, sir, the third equation will come from constraint. What sir? 2t upwards, a2 upwards. So 2t * a2 + t * a1 = 0. t common factor will come out and go home. 2a2 will come out to be equal to a1. These are your two equations and this is your one equation below. Three equations, three unknowns. Solve and get the answer. Now it's easy to say solve and get the answer. Okay? But the problem comes in solving. Still, if any child adopts this path, I will show him how to solve it. Whenever it comes like this, always try to reduce the number of variables. Try to have fewer variables in front of you. Okay? Like here, check it. Here you can do one thing. If I say this in this question, if I assume a2 as a. Let's assume a2 as a, then a1 will be 2a. They will say yes, sir. I said, now put this value here. So this equation will become how much? 4mg - t = sir, 4m * a1. a1 is how much? 2a. So put the value of 2a here, it will become 8m. Write its equation. What will you write? 2t - mg. Sorry, I forgot to write this here. Okay? Equals, what will you write? m * a2. What is the value of a2? a. So this will become m * a. I think now you can solve the question very easily. Now there is no difficulty left in the question. What do you have to do? Eliminate t. So multiply this by two. Assume you multiply the entire equation by two. As soon as you multiply the whole equation by two, it will become 8mg. This will become - 2t. This will become 8 * 2 = 16m. Now what will you do? Add all of them. As soon as you add, look, 8mg minus mg is 7mg. I said okay, brother. t is canceled out. And this will come out to be 17m. m cancels out m. a will come out to be 7g / 17. But after this, another mistake happens. Sometimes they ask for its acceleration, and we calculate its acceleration. Or they ask for its acceleration, and we calculate its acceleration. So, as our a has come now. Now what is a? a is a2. So this is a2. What does a2 mean? This is its acceleration. So if I ask you to tell me a1, then you will write, my brother, a1 = 2a. What does 2a mean? Sir, this will come out to be 17g / 17. Are you understanding? Clear? So this is basically our method. This is how questions of this type are often solved in books. But now let's move to the SKC method. Salim Bhaiya's method. Okay? Because, as you can see, this is not an easy thing. This is quite a long thing. In this, you first write this first equation, then the second equation, then the third constraint equation, then write one variable. Now, sir, now, sir, there are two blocks, so three equations are formed. Suppose there were three blocks, then four equations would be formed, and if there were four blocks, then five equations would be formed. Are you understanding what I am trying to say? Okay? So brother, then brother, it becomes more complicated. So brother, if you solve those questions with math, it will take a lot of time. But now, in Salim Bhaiya's style, see how quickly you will solve the question and get out. Look carefully. What do they say? I said, in such questions, do one thing. What? I said, first, assume its acceleration is also upwards, a1, and assume its acceleration is also upwards, brother, this is given as a2. Okay? So now we will also write it as a2. Assume the acceleration of this is also upwards, a1, and the acceleration of this is upwards, a2. Assume the acceleration of both is upwards. Now you will say, sir, this is wrong. How can the acceleration of both be upwards? I said, I don't know if it can be. Then why are you assuming it? What did I tell you in constraint motion a little while ago? If the acceleration is assumed incorrectly, the question will not be wrong, right? Then the answer will come negative. So I am saying the same thing here, that brother, assume both are upwards. I know one of them will be negative, it will come on its own. Whichever comes negative, we will understand, brother, that we have assumed its direction incorrectly. Is it clear? Okay, sir. So now they say, okay. Let's assume it. After this, I said, let's assume the tension here is t. tt tt. So the tension here will be 2t. I said, yes. I said, start with the constraint motion equation. Okay, sir. Okay. Constraint motion equation means, sir, 2t * a2. Okay, sir. + t * a1 = 0. Meaning, you can write this directly after a while. If you eliminate t, then 2a2 + a1 = 0 will come. Any problem? They will say no problem. Now let's move to its next part. So if I talk about its next part, I said, let's put the values. Now, meaning, you start from here itself. You start from here itself. Now, do you know the advantage of this? In one line, your tension will come out. How? They will say, sir, now put the values here. Look, what is it? Two. What will a2 be? a2. Sir, the force above minus the force below, divided by mass m. What is the force above, my brother? You will say, sir, the force above is 2t. The force below is mg, and the mass is, suppose the mass is given as m. Plus, what is a1, brother? Sir, the force above is t, minus the force below is mg, divided by the mass below, what is it, my brother? Sorry, the force below is 4mg, brother. The force below is 4mg, divided by its mass below, what will it be, my brother? 4m = 0. Now look, solving this, I think it is much easier than these. We had to do all this. From here, now look, t is visible in one line. Okay? In one line, t will come out. After this, when you are solving on pen and paper, look, m, this m, it has gone common there. Okay? This is four, so multiply the entire equation by four. Multiply by four. This, this will also disappear. Okay? This becomes how much? 4 * 2 = 8. Send 8 inside. 8 * 2 = 16t - 8mg. Okay, brother. + t - 4mmg. So tell me, 16t and one 17t. So this means t will come out to be 12mg / 17. Very easily made. Very without any difficulty, you have found its tension, and once you have found the tension, now whatever you want, you can find the acceleration of whoever you want. If you are asked to tell me a2, what will a2 be? Or tell me a1, what will a1 be? a1 will be directly said, sir, the force above, the tension, which is 12mg / 17. The force above minus the force below, divided by total. Are you understanding? Okay, sir. Okay. You know what the advantage of this method is? Whichever acceleration is asked, that will come out directly. Meaning, if it is asking for its acceleration, then there is no need to find this. But in this, what was happening? In this, all the equations were solved, and all the terms were coming out. Okay? When you are solving from here, a is coming out. a1, a2, a1, a1 is coming. Then you will also have to find a2. Okay? If suppose you want its acceleration, you have found this, then you have to go from here to here. But in this, find the value from where you want it. So look, mm will cancel out from here. This will become how much? 17 * 4 = 68. Everything from 52 to 68. Okay? This will become how much? Sir, 52 minus 68, this will become sir, 56. 56. From here it will come g / 17 * 4. Divide this by four. What will this become, brother? We are going correctly. We are going correctly. We are going correctly. Yes, brother, we are going correctly. So this will become 14. 14g / 17. This is the acceleration a1. This is the acceleration a. This is the acceleration of a1. So look, here also we got 14g / 17. Personally, I don't think this method is bad. I won't call it bad. For those whose math is good, it is good. But if you want to solve quickly, then this method is the best. Assume the acceleration of everyone upwards, and after assuming the acceleration of everyone upwards, quickly tell me t1 a1, t2 a2, t3. Like, look at another question. Look again. Like this question. Okay? Tell me, find the acceleration. Let's assume its acceleration is upwards, a1. Let's assume its acceleration is upwards, a2. Here tension t, 2t, 2t. Okay, okay, sir. What will you write? Start with constraint. 2t * a1 + t * a2. Look, the advantage of assuming upwards. The advantage of assuming acceleration upwards is that all your terms will come in positive. Some plus-minus, when there is minus, that's when there are chances of mistakes. Here, there are no chances of mistakes for you. Okay? t has come out as common. So you will directly say 2 * a1. What will a1 be? Sir, its a1 will be. Upward force minus downward force minus 100 / 10. Plus, what will a2 be? a2. t - 40 / 4 = 0. Look, in one line, t has come out. Are you understanding? In one line, t has come out. What should we do? Multiply by 40. Now, as soon as t comes out, suppose the value of t is, say, 50. So look, a2 is very quick. You will directly find it. Sir, 50 upwards, 40 downwards. Okay? So the net is 10. Divided by mass, it's 2.5. So like this, you can do the question. Is it clear? If t has come, then now you can find both a1 and a2. Like, talk about this. Brother, now you do it directly. Assume tension is t. So this tension will be 2t. Okay? Now look, directly. I want the one-line method. What will you write? 2t * its acceleration. Okay? Let's write the full thing first, then I'll teach you to write directly. Look, 2t * assume its acceleration is upwards, a1. Its acceleration is upwards, a2. So what will you write? 2t * a1 + t * a2. Okay? Let's write it again. 2t * a1 + t * a2 = 0. t common factor has come out. Yes, sir. 2 * a1 has come. What will a1 be? Sir, a1 will be written as 2t - 10 / 1. Plus, tell me, what will you write for a2? a2. I said, write a2 as t - 20 / 2. Equals 0. Look, the story is finished. Multiply by two quickly. Multiply by two. Tension will come out immediately. Okay? And once the tension comes out, then you can find anything. Let me solve it once. Multiply everything by two. So multiplying by two, it will be cleared. 2 * 2 = 4. Send 4 inside. 80 - 40 + t - 20 = 0. So t will come out to be 60 / 9. Okay? 60 / 9. So this means tension is 20 / 3. So now you tell me, what do you need? Do you need a1? So brother, find a1. What will you write for a1? They will say, sir, a1 is now, 1 minute. Is it going into equilibrium? t = 20. 2t. Yes, it's not going. Okay? What will you write for a1? The force above. What is the force above? 40 / 3. Look, it's 2t, right? It's t / 3. So what will it be? 40 / 3 minus the force below. What is the force below? 10. And what is its mass? Let's solve it, brother. The answer will come out. The answer is going as 10 / 3. The acceleration of this is 10 / 3. It is given as g / 3. Okay? Its acceleration is g / 3. It is 10 / 3. So like this, you can do it. Now there are only two blocks, brother. Assume you have added more blocks. Added three. No problem. So three, you add 50. Assume its acceleration is upwards, a1. Assume its acceleration is upwards, a2. Assume its acceleration is upwards, a3. Here tension is t, and here tension will be 2t. What will you write, sir? t * a1. t common factor has come out. Plus 2t * a2. Okay? This t has also come out as common. t * a3 = 0. Take t common. Now put the values. Tell me, what will you write for a1? Sir, a1 will be written as t - mg / m. Okay, brother. 2 * a2, what will you write? a2. Sir, for this, you will write 2t - 2mg. I said, okay, brother. / 2m. I said, very good. Plus, what will you write for a3? a3. You will write, sir, t - 3mg / 3m = 0. Solve for tension. And solve for tension. So now you, now understand, if you were doing it the other way, then three equations, three accelerations, and one tension, four variables, your four equations would be formed, and solving four equations, brother, would be a disaster. But from here, tension will come in one line. And if I ask you to tell me its acceleration, you have found the tension. So what is the force above? Minus the force below, divided by mass. Quickly, the answer will come. Are you understanding? All though, usually you will see only two blocks. I will make one thing clear to you. Usually you will see two blocks or up to three blocks in HC Verma. But if you understand this method, then brother, all your fear of pulleys will disappear. Whether there are three blocks, four blocks, 50 blocks, you will do all of them. After this. Look, like, see more. See more. See more. See more. See more. See more. Like more questions. Okay? Like, I'll just pick a big question directly. Suppose. I said, I said, look, there are so many blocks. I said, now tell me. Tell me the acceleration of all of them. They said, tell me the mass. I said, let's assume, brother, its mass is 2 kg. Let's assume its mass is 4 kg. Let's assume its mass is 1 kg. Let's assume its mass is 2 kg. I'm just writing like this. Its mass is 4 kg. Its mass is 2 kg. Its mass is 4 kg. Now tell me, tell me the acceleration of all of them. Okay? So you will say very calmly. You will say, oh sir, let's assume its acceleration is upwards, A1. Let's assume its acceleration is upwards, A2. Its acceleration is upwards, A3. Its upwards, A4. This question will never come in the exam. It will never come. It will never come in life. But why are you doing this question? So that your fear goes away. And from today, you will solve these questions yourself with a smile. Whenever this, this is too many pulleys, it will never come, I'm telling you. But but once you understand this, it means after this, all the remaining questions will seem how to you, my brother? Very easy. Now look, see the tension. See how the tension will act, brother? Assume the tension here is t. t. This t. This t. So this is 2t. Okay? This is also t. This is also t. Look, t. So this is 2t. Now look, 2t, 2t, 2t. 2t, 2t, 2t, 2t. 2t, 2t, 2t. This is 4. I just practiced this. This is also 2t. This is also 2t. This is also 2t. I said, okay, brother. Here also tension is 2t. This 2t, this 2t, so this is 40. 40, 40, 40, 40, 40, 40, 40. This will be your 40. Check it. This is 40. So this is 2t. And this is 2t. This is 40. This is 40. So this is 8t. Okay? Okay, sir. Now tell me after this. What will you write, sir? 2t * a1. So look, how I will write. t has come out as common. 2t * a1. So 2 * a1 has come. What will a1 be? Sir, you will write 2t - 20 / 2. Plus, tell me about this. Sir, sir, 2t * a2. t has come out as common. * a2. What will you write for a2? Upward force minus downward force, divided by mass m. Plus, talk about this. Sir, 8t * a3. 8t * a3. t has come out as common. Okay? So what will a3 be? 8t - 10 / 1. Plus, talk about this. Sir, 2t * a4. 2t * a4. 2t * a4. t has come out as common. What will a4 be? Upward force minus downward force, divided by mass m. Plus, for this 4 kg, what will you write? 4 * a5. What will a5 be? Sir? Upward force - mg / its mass m. Plus, talk about this. Sir, this will be t * a6. So t * a6. t has come out as common. What will a6 be? Sir? t - 20 / 2. Plus, talk about this. Sir, for this, 3 * a3. And 3 * sorry, a7, whatever it is, acceleration. And this will be 3t - 40 / 4 = 0. Now check it. Directly multiply this by four. If the question comes in the exam, it will be solvable. You directly multiply this. As soon as you multiply, t will come out in one line. I know it is a little calculative, but no problem. If you find that tension, then it means if you have found the tension, then you can find the acceleration of whoever you want. Why sir? Upwards is 3t, downwards is 40. Find the acceleration. You will know the acceleration of every person. But such a question will not come. Sir, why are you doing this? I said, I am doing this because if you do this, then this question will seem very easy to you. And open your notebook and see. The most difficult question in HC Verma is this. Okay? In constraint motion, the most difficult question of HC Verma is this. Now see how easy it will seem. They will say, sir, assume its acceleration is a1. Assume its acceleration is upwards, A2. Assume its acceleration is upwards, A3. Here tension is T. Assume tension is T here. So this t, this t, so this is 2t. So for this, what will you write? For this, you will write 2t * a1. Plus, for this, what will you write? t * a2 + t * a3 = 0. Tell me now. Tell me, what will you write here? What will a1 be? Sir, a1 will be written as 2t - 10 / 1. Plus, tell me, what will you write for a2? a2. a2 will be written as t - 20. t - 20 / 2. Plus, what will you write for a3? t - 30 / 3 = 0. Done. Now take the LCM. Six will be the LCM, or directly multiply everything by six. Tension will come. Whichever acceleration you want, find its acceleration. And after solving in HC Verma, verify your answer. And when the question is done, definitely type in the comment box below that yes sir, we have done all the HC Verma questions.

We have completed the tasks using your method. Do you understand? Now let me show you more questions from HC Verma. Okay? Look more, look more, look more. These are questions from HC Verma. See, I solved them here. See? For example, this question about the inclined plane, we will look at that too. Wait, I had put the screenshot. Okay? I solved these. I solved these. Where did they go? Where did they go? Where did they go? Where did they go? Where did they go? Oh, where did they go? Where did they go? Where did they go? Huh? Here they are, here they are. It seems they flew away, brother. No problem. I will definitely solve them. No matter what happens. Here you go. This is called flying away. No problem. I will solve them now. I will solve them now. Okay. Hold on, look. Okay. Wait a minute. I will solve them now. Yes. Okay, brother. Look, for example, this question, look. Now you tell me. These questions will seem very easy to you now. Okay? Now you can solve them at a glance. For example, the question is. You say, sir. Now we will write directly, sir. Let the acceleration of this be a1 upwards. Let the acceleration of this be a2 upwards. Tension here is t, so this tension will be 2t. What will you write? 2t * a2 + t * a1 = 0. Sir, tell me, what will you write for a2? a2, I said, upward force minus downward force / mass m + a1. What will you write? Sir, upward force minus downward force / mass m = 0. Tension has come out. Tension has come out, so brother, now you can find everything. Do you understand? For example, this question is done. For this question, assume its acceleration is a1 in the forward direction. Assume its acceleration is a2 in the upward direction. Everything is upwards, assume everything is upwards. The advantage of assuming upwards is that the calculation will be easier. Now look, tension here is t. Okay, tt. I said yes. So what will be the tension here? It will be 2t. So what will you write? t * a1 + 2t * a2 = 0. What will a1 be, sir? What will its acceleration be, sir? Only one force is acting forward, t. So t / its mass / 2. What will you write for a2, sir? Upward force minus downward force 50 / mass m = 0. Brother, multiply everything by 10. Your tension will come out with great love. And if tension comes out, you can find everyone's acceleration. This is your homework. Not only this. It is possible that he tells you that we have placed it on an inclined plane. For example, if it is placed on an inclined plane, then no problem. If it is placed on an inclined plane, so what? mg sin theta will act in this direction. End of story. You say how will you do it? You say, sir, assume tension t is acting on this, tt. So this becomes 2t. Assume its acceleration, my brother, is a1 in this direction. Assume its acceleration is a2 in the upward direction. So what will you write? t * a1 + 2t * a2 = 0. I took t common. Now tell me, sir, draw its free body diagram. Sir, how much force will be acting here? I said mg sin theta will be acting here. Theta is 30°, so this will be mg / 2. Okay? So look, I will write directly. What will you write for a1, sir? Forward force minus backward force / mass m + 2 * a2. What will you write for a2, sir? Upward force minus downward force. How much will the downward force be? 2mg / mass m. Here you go. The question is done. The calculation for this is also easy. Look, cancel two with two. m is taken common and goes there. Right? The calculation for this is also easy. Look, check if there is any mistake, brother. 2t - 2mg = 2m / 2m. I said okay, look how easy the calculation is. Look, this mm cancels out. This two cancels out with two. What is this? t, 2t, 3t. Okay? 3t will be equal to how much, sir? This is half and this is two. So this will become two and a half. Two and a half means 5mg / 2. So these two go down. Two goes to three. And what will this become, brother? If I am not making any mistake, then t will come out to be this much. And if tension comes out, you can find anyone's acceleration. Do you understand? Is it clear, brother? I am telling you seriously. Look, look at an advanced question. This is a JEE Advanced 2019 question. Do you understand? I have copied it as it is from the website. Sir, this is a JEE Advanced 2019 question. Now in this question, he has asked. He has given four options. Although this question is mixed. In this question, concepts of work-power-energy and other things are being used. But tell me, if this block is moving forward with A1, then if I assume tension T here, assume tension T here. TT, so this tension will be 2t. So its acceleration forward, sorry. So tension will be acting forward, 2t. So the net internal work done by tension is zero. We saw that. So what statement will I write? 2t * a1. Okay, sir. For this, sir, its acceleration is downwards, -t * a2. Sir, its acceleration is upwards, tension is upwards, - t * a3 = 0. As soon as you solve this, 2a1 will come out to be equal to a2 + a3. The specialty of this question was that as soon as you see this question, look at its fourth option, it matches. This fourth option matches. Look, take a1 to the other side, bring this to this side. So what will a2 + a3 be equal to? It will be 2a1. So that's our fourth option. The specialty of this question was that all the children who attempted the other four options, the first, second, third were wrong. Okay? So what do smart children do? Smart children first attempt the easy questions. They see it and think, wow, this looks very easy, let's do this first. They tick it and look at the rest, oh, in the rest, we will have to find the extension, apply the work-energy theorem. Okay? And maybe concepts of SHM, SHM are also being used. Let's leave the rest of the questions for later. Tick one correct question and move on. And later it turns out that this was a four-mark question, it was in multiple choice, and it turns out that only one option was correct, so you get four out of four marks. So overall, I think with the concept we have seen here, you can easily solve the questions that I have just taught. Do you understand? For example, look at more questions. I have kept many questions for you. For example, take this question. Okay? Suppose I tell you here, suppose its mass is m. Suppose its mass is 2m. Suppose its mass is 4m. Tell me, assume the acceleration of each person is A1 upwards, assume acceleration is A2 upwards, assume acceleration is A3 upwards. Assume tension T here, t. So this will become 2t, t. So this will also be 2t, and this will also be t. So what will you write? You will write directly t * A1 + What will you write for this? 2t * a2 + What will you write for this? 3t * a3 = 0. And as soon as you solve this, what will a1 be equal to? t - mg / m + 2 * a2. What will it be equal to? 2t - 2t - 2mg / 2m. Here you go, brother. And what will you write for this, sir? Sir, we will write 3t. This three comes as it is. What will a3 be? 3t, 3t, 3t, 3t - 4mg / 4mg / 4m = 0. Done. Do you understand? Okay? After this, now look, you will be able to solve countless questions. I have full confidence. Now I am giving you. I am attaching quite a few questions from books here for your practice. Okay? Of every type. For example, in this, you have to find a1, a2. Okay? You practice these questions, brother. Okay? Here, for example, he said, find the acceleration of the block. Okay? Here he asked what will be the acceleration of a1, a2, a3? We have already seen this question. For example, this question. Tell me, what will be the acceleration of each of these? Okay? You try these questions, brother. But now I have full confidence that no matter what question comes in front of you now, you will solve the question well. Your fear must have gone away, brother. Look at such questions too. Look at this question too. You will find these types of questions in HC Verma. Sir, how to do it? I said, brother, assume its acceleration is a1 in the forward direction. Assume its acceleration is a2 in the upward direction. Assume upwards. Okay, sir. Tension here, tt, tt, and tension here will be 2t. I said, okay. What will you write? t * a1 + 2t * a2 = 0. Okay, sir. Sir, what will you write for its acceleration a1? Sir, how much force is acting forward? t. What is the mass? Four. Sir, there is no force backward. I said no. Suppose friction was given, then we would write the friction from behind here. Okay? We would do forward minus backward divided by mass. End of story. So if you had done the friction question. Anyway, let's move on. 2 * Sir, what will you write for a2? a2, a2. I said upward force minus downward force / mass m = 0. Solve it, you will get tension. If you get tension, then you can solve all the questions from there. Do you understand? Is it clear? Okay, let's look at questions on PYQs too, we will see what kind of questions are asked. I think after this, you must have understood the concept clearly, that now I can solve any type of question. One more question, brother, one more question, suppose I give it like this. Okay? Now, now I hope you have understood enough that you have learned to write the answer statement in one line. For example, let's talk about this. Suppose the acceleration here is a1. Its acceleration is a2 upwards. Its acceleration is a3 upwards. Tension here is t, tension here is t, so tension here is 2t. Now look, I will write directly. 2t * a1. 2t * a1. It will be 2 * a1. What will you write for a1? Pulling force minus resisting force, mg sin theta will act backward, how much divided by total mass? Here you go. Plus, what will you write for this? t * a2. t is taken common. What will you write for a2? t - 2mg / 2m. Plus, what will you write for this, sir? t * Sir, a3. a. t is taken common. What will a3 be? t - mg / m = 0. Multiply by two and relax. Clear? So now if this brother, this concept is completely clear to you, you have gained full confidence, then type Yes in the comment box below. Look, this is a recorded session, not a live session. If you were in front of me, I would have asked you live. Okay? I would have conducted polls too in a live session. But here there are no polls, and no live chat. So I would like you to type in the comment box with an open heart. All the children who have watched this lecture so far, pause the screen now and tell me with confidence that Yes sir, no matter how many blocks, no matter how many pulleys, our fear is gone now, we will solve whatever question comes. If you feel this way, then type in the comment box right now. And yes, I would like you to definitely solve all the questions from HC Verma. Solve all the questions of constrained motion. Clear? Okay. And yes, Kaddu Gang OP. Do you understand? Okay? All the children who are joining our class, all the children who are falling in love with physics from this class. You all have joined the Kaddu Gang. Do you understand? So type this too, so that I can also see how many children this lecture is reaching. Okay? Let's note it down if anyone wants to. Yes. Okay, brother? Now, some profile questions also come in this. For example, this one. Sometimes what happens is that the block is missing. So I will explain it to you through an example. Okay? Sometimes the block is missing. I don't understand, man, this person is going down with one, this is going with two in this direction, so with how much will it go up? So in such questions, I will tell you to quietly assume a block here in your mind, and if this is missing, then assume a block here too. Okay? So your question becomes like this: If this point is going down with one, then this block must be going down with one, and if this point is going with two in this direction, then this block is going forward at 2 meters per second. So in that case, you will simply say, sir, assume tension t here, so t, and what will be the tension here? 2t. So suppose it asks for its velocity or acceleration, you can directly write tension backward and this forward, so - t * 2. Sir, assume its velocity is v upwards, so + 2t * v. Sir, tension here is upwards and this is downwards, - t * 1. As soon as you solve this, it will be equal to 0. t will be taken common. So b = 3/2. Sir, b = 3/2 came out positive, which means it will move upwards with 3/2. So what I mean is, suppose he said that there is a rope, this point of the rope is going with this much. Okay? So don't take tension. Assume a block there. Assume an imaginary block. Okay? And solve it by assuming the same velocity or acceleration for the block. For example, let's look at another question on this. A question, for example, this one. Okay? He is saying, brother, this is going forward with u, so tell me how much will this go forward? So you do one thing, brother, assume a block here. Here, assume a block like this. Now tell me, if this point is going forward with u, then the block will also go forward with u, right? This is the condition of the rope. I said, work is done. Assume tension t on this, tt. So tension will be 2t backward. Now play the game for the block. Sir, this is going forward with b, suppose. So what will you write? v * t. I said, okay. For this, sir, - 2t * u = 0. t will be taken common. What will v be equal to? It will be 2u. Velocity of the block attached. End of story. Do you understand? So you can solve the question by assuming it like this. The same is true for acceleration. Suppose I say this, this acceleration is given. Its acceleration is given as a. So what will its acceleration be? It will be 2a. Acceleration. Clear? Okay? After this, now you have a small article left, which is called rocket propulsion. Okay? In rocket propulsion, you just need to remember one thing: if I say, a rocket is going upwards and emitting smoke from behind. Okay, sir, everything? When smoke, smoke means its fuel is coming out from behind. Continuous fuel burning, sorry, fuel is not coming out. Fuel, fuel is burning, due to which smoke is continuously coming out from behind. I said, okay, brother. Okay. So like you see during Diwali. During Diwali, we don't light firecrackers and rockets, so what happens is that smoke is coming out from below, and brother, the rocket flies upwards. It's kind of a similar thing you see here: if smoke is continuously coming out from below, then due to that, a thrust force acts upwards on the rocket, whose value is v relative * dm / dt. Do you understand? v relative * dm / dt. Here, dm / dt is the rate at which your fuel is burning or the rate at which its mass is decreasing, and V relative is the relative velocity with which the smoke is coming out from here. Do you understand? So this thrust force acts upwards. Now, how this formula came, there is a long derivation for it, which we see in center of mass. Okay? You can skip that derivation for now. Just remember this formula: F thrust = v relative * dm / dt. For example, let me give you some questions on this so that you get an idea. For example, look at the question. The question is: Gases are ejecting at a rate of 1 kg/ second. Find V relative for gas to have an upward acceleration of 2G. Meaning, brother, this is a rocket. Gas is continuously coming out of the rocket. It says, brother, tell me with what relative velocity should the gas come out so that the rocket has upward acceleration? So what will you say? Sir, if I draw the free body diagram of the rocket, a thrust force will act upwards. I said, okay. Sir, mg will act downwards. I said, okay. So now you say, sir, how much force is acting upwards? f thrust. How much force is acting downwards? mg. Upward force = upward force - downward force = mass * acceleration. I am saying this for the initial stage because the rocket is on the ground now, it has to be lifted. It has to be lifted up now. So, as they say, to launch a rocket, at what rate should the gas come out? Okay? Okay, sir. How much will f thrust be, sir? b relative * dm / dt - mg = m * a. Take this to the other side. So b relative * Sir, how much is dm / dt? dm / dt is 1 kg/ second. Equal to, how much is the mass, brother? Mass is 1000 kg. So this will go there. This will become sir, mg. Let's write it completely. mg + a. As soon as you put the values, what will v relative be equal to? 1000. Value of g is 10, and what is the acceleration, brother? 20. The acceleration is to be 2g, so it means 20. It means it will come out to be 30 followed by 3g. A good velocity has come. Do you understand? Clear? For example, look at another question. Look at it with proper language. For example, this is the question. He said, rocket with a lift of mass so much. Brother, a rocket. It has to be lifted. Its mass is given. Is blast off bird with an initial acceleration of 10. Brother, it needs an acceleration of 10 upwards. How will you give it? How will you give it? Sir, from below, sir, you will emit smoke from below like this, due to which thrust force will act upwards. He said initial thrust. You have to pull it. So brother, tell me, you will apply f thrust upwards. I said, okay, brother, you will apply f thrust upwards. mg force is acting downwards. I said, okay. So to give an acceleration of 10 upwards, what will I write? Sir, f thrust. Upward force minus downward force = mass * acceleration. So how much will f thrust be, sir? It will go to the other side, mg + ma. Sir, the value of a here, here take m common, sir, g + a. As soon as I put the values, m is how much, sir? 3.5. I said, okay, brother. 3.5 * 10 to the power 4. Sir, g is 10, and a is also 10, so this will become 20. Your answer will come out to be 7 * 10 to the power 5. Do you understand? Yes, this is your f thrust. If f thrust comes out, and if he says, suppose b relative is 500, then tell me what dm / dt should be. After this, the question will proceed. At what rate should the gas come out? So he has given it. He has given b relative. He will say, at what rate should the mass decrease? So the value of f thrust, put b relative * dm / dt. In fact, in reality, what is this relative, in reality, if you study physics properly, then when you see the full derivation, this is the velocity with respect to this rocket. Do you understand? Okay? Let's move on. After this, let's look at one more question. Let's look at one more question. Everything is written here. Sorry, I just found this quickly, so I put it here, so that I can give you one more question. So in this, a 6000 kilogram rocket is set for vertical firing. This is a rocket, brother. We have to take it upwards. Okay? Exhaust speed is 100 meters per second. Meaning, sir, in this, it means V relative has been given. Sir, V relative is how much? Sir, V relative is given as 1000. Okay? How much gas must be ejected each second? He is asking, brother, tell us how much gas we should eject in one second? dm / dt, how much should we eject? To supply the thrust needed to give the rocket an initial upward acceleration of 20 meters per second square. Brother, it needs an acceleration of 20 upwards. So how much here, we need to eject gas at what rate? So brother, if you give acceleration upwards, mg is acting downwards. So it means upwards, what will act? f thrust. f thrust. Who will act downwards? mg = mass * acceleration. What will f thrust be? Sir, f thrust will be sir, v relative * dm / dt. I said, okay, brother. Take this to the other side. mg + a. Okay. Sir, how much is v relative, brother? How much is v relative? I said 1000. How much is dm / dt? How much is dm / dt? Sir, dm / dt is unknown. I said, okay, brother, this is what we need to find. How much is the mass? How much is the mass? 6000. I said, okay. How much is g + a? It will be 30. g is 10, and this is 20. As soon as you solve this, cancel three zeros with three zeros. 6 * 3 = 180. They have given the answer as 178. Yes, because they have given the value of g as 9.8. Clear, brother? Okay. So, my brother, for today's part, we will leave it at this, keeping this time duration in mind. Okay? Keeping this time duration in mind, we have covered many things here. My brother, keeping this time duration in mind, we have covered quite a few things here. Okay? We have looked at all the forces. Tension force, mg force, spring force, pseudo force. Okay? We have studied all these things. We have also solved equilibrium questions in abundance. After that, we also solved pulley equilibrium questions in abundance. We have also solved constrained motion questions, quite a lot. Then we have also done the questions related to acceleration, pulling force minus resisting force, quite a few. We have also seen many questions from HC Verma here. And after that, the questions related to spring force, or other types of questions, monkey questions. Okay? I have covered almost all types of questions here, especially constrained motion, no matter how many pulleys or how many blocks are involved. Now I have full confidence that you will solve the questions. And sorry, one more thing is left, man. One more thing is left. One more thing just came to mind. You said what? I said, brother, always remember this: the way to ask for tension is that they put a spring balance system like this. Okay? Okay? They put a spring balance system like this here. If they want to ask for tension, they will put a spring balance system like this and ask what is its reading. So remember, the reading of this is, the reading of the spring balance gives the tension. Similarly, the way to ask for normal force is a weighing machine. When we go to the doctor's shop, there is a weighing machine like this. When we go to the shopkeeper's shop, there is a weighing machine. He weighs by placing things on it. Okay? So this does not read mass. It reads normal force. Meaning, if in a question they say that brother, tell us the reading of the weighing machine, then understand that they are asking for normal force, and if they say reading of the spring balance system, then understand that they are asking for tension. Clear? So, I will complete today's session here. Please solve all the parts that I have taught you in this session, if possible. Also, solve the questions from HC Verma. That will give you confidence. That will also sort out your silly mistakes. Your calculation will improve. I have done everything that could be done in the given time. And your equilibrium questions, pulley questions, constrained motion questions, friction. Friction is left. We will cover the friction part in the next article. If you have understood everything after this, then type in the comment box with an open heart. Do you understand? After this, you can solve all the questions. I will say again, we will cover collision questions in center of mass, and we will cover the friction part in the next lecture. Do not have any confusion about this. And if you have understood everything I have taught, then type in the comment box. And brother, Kaddu Gang Yes OP, and Kaddu Gang should also be buzzing below properly. Okay? You can join this Telegram group. I will upload the PPT of this lecture here, and I will also upload other important topics here. Okay? And if you are on Insta, you can join Insta. Okay? I will not force you for this, but please join this, because here I upload all your important things from time to time properly. Take care of yourself, and keep working hard.