Units and Measurements🔥 | CLASS 11 Physics | Complete Chapter | NCERT Covered | Prashant Kirad

Burnt is called fire, extinguished is called ash, and one who makes physics easy is called Prashant Kirad. So, hi everyone, first of all, I welcome you all, your own Prashant Bhaiya, and I have arrived with your demand, meaning, whatever you asked for, I have given you. What was your demand? That you conduct one-shot lectures, and that too for every chapter of physics. So, from today, those one-shot lectures have started. This is our first lecture, which is Units and Measurements. It is a very lovely, very simple, very excellent chapter, right? First of all, I know you must be very excited. You must have definitely studied with me in 10th grade, and you must have enjoyed it. Now it's the turn of 11th grade, right? What did you think? That Bhaiya won't return after 10th grade? Oh, Bhaiya will definitely return, right? Prashant Bhaiya is standing with you, so why be afraid? Meaning, you have finally entered 11th grade, and you are going to study this chapter. First of all, what all am I going to teach you in this chapter? I am going to teach you all those topics that are according to the latest syllabus. I will teach you all those topics. Let me tell you, in your latest syllabus, there used to be a topic called parallax, which has been removed. Whereas, according to the new syllabus, there is a topic called error, which is included in your syllabus. So, I will teach everything, I will teach in detail, and that too in a fun way. First of all, tell me, what is the Josh Meter, the energy level? Is it the same energy as before, or have you become deflated after coming to 11th grade? Is it a dream, a goal, to make this class excellent like 10th grade? If it is a dream, if it is a goal, then write Josh Meter once. What is it? It should be 1000. I need double the energy in you than I have in me. Come on, let's start. Further lectures will also keep coming. It will take some time, but the lectures will definitely come. Shall we start? Come on, let's start this chapter from a very basic thing, which is, what is a physical quantity? Bhaiya, what is this physical quantity? Oh, foolish child, I call you foolish affectionately. Come on, you already know, you have studied on your own, right? Foolish child, I say it affectionately, okay? So, what is a physical quantity? A physical quantity is something that we can measure, that we can quantify. For example, what is my weight? My weight is 70 kg. 70 kg. What will I say? I can measure my weight. You will say, absolutely, you can measure it. But can you measure your feelings, your feelings for your crush? Yes, you can absolutely measure them. How? Tell me. Infinity. I'm kidding. Meaning, we cannot measure feelings, right? It's a different matter that the feeling your crush has for you in their heart is zero. I'm telling you the reality. No problem, son, it will hurt, but it's real, right? It's zero in their heart, but it's a different matter that we can never measure feelings. So, the things that we can measure, we call them physical quantities. So, physical quantities refer to any property of a material or a system that can be measured, that can be quantified. For example, length, weight, all these things are your physical quantities. Now, look, a physical quantity has two components. What are the two components? The first component is the numerical value, and the second component is the unit. I will explain, understand carefully. I am asking you, what is your weight? You said, Bhaiya, my weight is 60 kg. So, what did you write? You wrote two things, son, two things. The first thing is this numerical value. What is this? Numerical value. And what is this? Unit. What is this? Unit. Meaning, every physical quantity is made up of two things. One is your numerical value, which we represent by 'n', and one is your unit, which we represent by 'u'. Simple. Is there anything new? Is there anything dangerous? Is there anything scary? Oh, are you understanding, foolish child? Very simple things are going on. Look, in this one-shot, everything is going to be covered. I will also practice questions. Almost all the questions in your exam will be of this pattern, which I am going to do today. Have a little faith. I know that since you came to 11th grade, one is that when we come to 11th grade, we are already very troubled. Why? Because our true friends, who were with us until 10th grade, get separated from us, they go far away. You miss them, right? You must be missing them. You are troubled, you have come to a new class, but don't worry, I will get it done, okay? So, how do we write? 'n' and 'u'. We write physical quantities like this, right? This is the numerical value, and this is the unit. Okay? But, Bhaiya, what is this unit? If I ask you to define unit, how will you define units? Tell me. How do you define units? Let's read about it. Come on. What are these units? First of all, what is this unit? It is a standard that is widely accepted and used to measure physical quantities. Meaning, it is a standard that is looked at all over the world, and according to this, any physical quantity is measured. For example, what is my weight? My weight is 70 kilograms. Can I write this in another way? How? Tell me. Can I write this as 70 thousand grams? Absolutely, I can. Why? Because I have changed the unit. What have I changed, son? The unit. Meaning, a unit is a standard that is used worldwide everywhere to measure things. Very good, understood. What is a unit? There is no need to explain it. It's a very theoretical thing, right? Sometimes they ask in school exams. Look, I don't know about school teachers. If a school teacher's mind gets tickled, you understand, you understand. If it comes to their mind, they will ask anything. That's why I want to cover everything, okay? Generally, it is not asked. What is the importance of a unit? A unit ensures consistency in measurements. First, the measurements that are coming should be equal, they should be consistent. That is one function of a unit. Very good. Next, they allow scientists across the world to communicate. Meaning, now, if I say my weight is 10 kilograms, right? If, imagine, there was no kilogram, and I say my weight is 1000. You think, 1000 what? Bhaiya, 1000 what? 1000 kilograms? I say, oh no, no, grams, grams, I was saying grams. Grams, right? Similarly, there is a ton. So, meaning, a unit is important for communication worldwide, right? What's next? They form the basis of calculations. Meaning, with its help, we can do calculations and comparisons, right? Very good, understood the importance of a unit. Very basic, basic importance, three. Let's talk about types of units now. Bhaiya, there are two types of units. Very simple, very, very easy ones. Which ones are they? The first unit is very lovely, which we call a fundamental unit, and the second is a derived unit. Fundamental? Oh, foolish child, it's nothing. Fundamental unit, the name itself suggests fundamental, meaning a basic unit. Look, a fundamental unit is a unit that we assume. We assume. Just like you assumed that they would reply to you, they won't reply, but you assumed. Similarly, fundamental units are units that we assume. We say, okay, son, right? So, basically, basic units are called fundamental units, and for your study, there are seven fundamental units. What are they? I will show you a table once. You already know these seven fundamental units, but I will tell you once again. What are they? Keep watching. First is mass. Mass is a fundamental unit. Okay, what is the symbol for mass? It's 'm'. Very good, very good. Now tell me, what is the SI unit of mass? What is the SI unit? What does SI unit mean? A standard unit at the international level that is used. So, you know that for mass, we use kg. Very good. Length. Length is represented by 'L'. What is the international unit? What is the SI unit? Meter. Very good. For time? Seconds. Very good. Current. Current, electricity, electricity. Where did you study it? In 10th grade. Now don't say that in 10th grade, Bhaiya was just having fun. I will hit you. I taught you, right? If not me, then someone else taught you. You studied, right? Come on. What is current? What is current? The unit of current is Ampere. What is Ampere? Represented by 'A' in both cases. Temperature. The SI unit of temperature, son, is what? Kelvin. What is it, son? Kelvin. Besides this, amount of substance. You will study amount of substance in 11th grade in a topic called mole concept. Maybe you have already studied it. If not, no problem, Bhaiya, right? So, what is it? We represent it by 'n', right? And its unit is what? Its unit is mole. What is mole? Right? Mole is its unit. One last thing is luminous intensity. You have never studied this. I will tell you. Generally, questions are not asked from this, but luminous intensity is a type of quantity. What is it? It is a quantity that tells about some things. You will learn about it gradually later. Let's not go too deep now. Okay? What is its unit? Remember its unit. What is its SI unit? It is Candela. What is it? Candela. Okay? These seven fundamental units are your seven fundamental units. Okay? Understood. Now, with the help of these fundamental units, we derive the rest of the units. Derive means to obtain. That's why we call them derived units. What do we call them, son? Derived units. Obviously, those units that we derive with the help of fundamental ones, Bhaiya, we will call them derived units. Is there anything new in this? Bhaiya, what is there? You were getting so worried. There was nothing like this, right? And son, understand one thing. I am teaching, but your focus should not be entirely on me, but entirely on the board. Your focus should not waver, otherwise, you know, I roast. Like one child was repeatedly asking me, what was he asking? He was asking me, Bhaiya, I get a little distracted by the opposite gender. So, I told him, son, first of all, put your real DP on your Instagram, WhatsApp, Facebook. The day you put your real DP, the distraction will end, because no one will message you. Study, okay? Otherwise, you will keep getting roasted for free by me. Come on. What is a derived unit? Derived units are the units used to measure derived physical quantities. Right? We derive the units of some different physical quantities from the help of fundamental units. For example, area. What is the unit of area? What is the unit of area, son? What is area? Length * breadth. Length * breadth. So, what is it? Meter square. Right? L squared comes, right, son? L squared. Length * breadth, meaning we are multiplying two lengths. One is length, one is breadth. Both will be in meters, so what will be the unit? Meter squared. Similarly, volume. What is volume? Volume is meter. So, what is it, son? Different, different, different derived quantities, we can also derive their units with the help of the fundamental quantities we just studied. Let's see some good questions for this. For example, the first one will be velocity. What is velocity? What is velocity? Tell me. Are you looking at my face? Didn't you study? Displacement / time. You studied it. Yes, I remembered, I remembered, right? What is displacement? Length. What is time? T. Now, tell me one thing. How do we say length? Meter. How do we say time? Second. Right? So, what will this be? Meter per second. Right? What was the unit of acceleration? Meter per second squared. Very good. We already know. Let's see a question. Write the SI unit of the following derived quantities. All these quantities are different from fundamental quantities. You can see them. Tell the SI unit of all of them and also the derived units. What is SI unit? SI unit, for example, the SI unit of force is Newton. The SI unit of pressure is Pascal. I am saying Pascal, not P, son, okay? Yes, okay. Pascal. Besides this, what is the unit of work? Tell me quickly. What is the unit of energy? Energy and work are the same. Joule. You know. Power. I taught you Watt in 10th grade. These are their SI units. I am asking for their derived units. Come on, quickly. Write the derived units in the comments. Come on. Yes, who all got it? Very good. Many children must have got it. For example, force. What is force, son? If you remember the formula for force, then you will know what force is. Mass * acceleration. What is mass? We measure mass in kg. What is the SI unit of acceleration? What is the derived unit? Tell me. What is it? Meter per second squared. If we multiply these two, then this will come. Kg meter per second squared. Yes or no? Understood. These are derived units. Very good. Look at the next one, Bhaiya. Look at the next one. What is pressure? What is pressure? Tell me. Is it force by area? Yes, it is. What is force? We have just derived its unit. Very good. Right? This has come. Very good. Now tell me, what is the unit of area? Meter squared. What is it? Meter squared. Right? So, this will go up. This will cut one from one. So, finally, what will come? Kg divided by meter second squared. Whose is this? This is of your pressure. The formula for pressure is this, son. Force by area. Right? So, this unit of pressure has been derived. Very good, very good. Is it clear up to here? There should be no problem, son. These are very simple things. There is nothing difficult that you are worrying so much about. There is nothing. Very simple things. Do you understand? Very good. Right? Come on, let's see the next one. What is the next one? Your work. What is work, son? If you remember, we studied that work is equal to energy in a way. The SI unit was Joule. And what was the formula for work? Force * displacement. Remembered? Now, look, we know the unit of force. Just multiply this by displacement, meaning square the meter. Can you do it? Now look at the next one. Energy and work are the same. Power. What is it, son? The basic unit of power is. Tell me. Oh, tell me, son. What is the unit of power? Watt. And what was its formula? We studied it in the electricity chapter. If you don't remember, no tension. It was energy divided by time. Energy divided by time. Meaning, we have already derived the unit of energy from here, right? We have derived the unit of energy and work from here. Just do what? Divide by time. Meaning, divide by seconds. So, like this, we can derive the SI unit of anything. You already know the SI unit. We can also derive the derived units. If any question comes, such simple, simple questions come. We will say, oh, bye-bye, good-bye. Right? We can easily derive it. Nothing to worry about. Don't take so much tension because these are very basic things. Come on, the next topic is. What is it now? System of units. System. Which system of units? Three types of systems are being used all over the world. Which systems are they, son? Let's see. The first one is the FPS system. Oh, this FPS is not that one. iPhone's 60 FPS camera? Oh, that FPS is different, son. This is different. Right? What is the FPS system? Understand this carefully. Understand this carefully. In this, we measure mass in what? In pounds. We measure length in feet. Don't we say how many feet? How many feet or not? We say it, right? And we count time in seconds. The second unit system comes, your system comes, the CGS system. What is the CGS system? Oh, C means what? C means, son, not what you are thinking. C means centimeter. Simple matter, right? Centimeter means here we will do length in centimeters. We will do mass in grams. And second is the same. The next thing is the MKS system. The MKS system is very important. Why? Because the MKS system is the SI system. Meaning, look, these are three basic systems. There is one system that is being used in standard places, right? It is being used standardly. So, that is this MKS. That is this MKS. Meaning, the MKS system, we use this in SI. Okay? In this, what is it? We count length in meters. Right? We count mass in kilograms. And we count time in seconds. What did I say? MKS system is very important. Understood. Done. Very good, very good. So, these were the three types of systems we had to study. I have told you in complete detail. Come on, let's move forward quickly. Now let's talk about what? Let's talk about some important things. For example, as I told you, if you look at the SI units, they are similar to the MKS system. Look, I have written it. Look, length in meters. What was length counted in in MKS? In meters. Right? Weight? In what? In kilograms. Look, son. Time? In what? In seconds. Okay? Meaning, the MKS system and the SI system are the same. Same. I have already told you the rest of the things. I told you this a little while ago. Come on. Now, our next topic comes, supplementary quantities. So far, what we have studied, I will show you numericals on this in about 5 minutes, but before that, let's study some supplementary quantities. So far, what have we studied? We saw the system of units. We saw three types of systems. Are they clear? Now, look. Now I will teach you two types of supplementary quantities. These are quantities, son, that are in between. Right? Like, isn't there that boy in your class who doesn't want to sit with the toppers, nor with the backbenchers? He will sit in the middle. He doesn't want to get full marks, nor does he want to joke around. Right? What do you call such boys? You know. Meaning.

In other words, supplementary quantities are those that are of a different type of quantities. The seven quantities I told you about earlier, the fundamental quantities, and the derived quantities, these do not fall into either of them. They say, "I will not go into fundamental, nor will I go into derived. Make a separate column for me, I am a supplementary quantity." Okay, so supplementary quantities are quantities that are not categorized in fundamental or derived. They are not in both, but they are important. Why? There are two types of quantities, understand. The first is the plane angle, and the second is the solid angle. You have studied this plane angle in Class 10th, in Maths. I am becoming a Maths teacher and taking away the jobs of Maths teachers. Remember, we used to draw a circle. Wow, I drew a crooked circle. This is the center, this is the center. Okay. From the center, look, it used to make an angle, it used to make an angle. Remember, it used to make an angle. In what did we measure that angle, son? In radians. In what did we measure it? In radians. Remember radians. And what is its formula? For those who don't know, I will tell you. The formula to find this angle is arc length divided by radius. This is the radius, this is the arc length. This is the formula. And this is what we call the plane angle. What do we call it, son? Plane angle. So, the plane angle has the formula arc length by radius. It will be useful in many places later, so remember it now. Okay. Apart from this, what is its SI unit? Its SI unit is radian. Radian. Very good, son. Look at the next one, solid angle. Solid angle is also the same thing, it's an angle. But now here there is no circle, brother. Now there is a sphere. What is it? Imagine, just once, close your eyes and imagine, son. Your imagination is very strong anyway. Imagine once, close your eyes, a sphere has appeared in front of you. Imagine, and an angle is being formed from the center, an angle is being formed. Can you imagine? So, that angle will be called what? Solid angle. And what is its formula? Its formula is what? Area of the surface. That is, how much surface area is it taking? Look from the center. Two lines went from the center. Now they will be covering an area. How much is that area? Divided by the square of the radius. What is its unit? Its unit is steradian. What is it? Steradian. Okay. No need to go into that much detail. Just understand this much: there are two types of supplementary quantities: plane angle and your solid angle. You must know this much. Okay, son. If you know the formula, that's great. Let's move on. Now we move to a very important concept from which a question will come in your paper, brother. Will you leak the 11th-grade paper too? It will come, I am telling you it will come in your paper, mainly in schools. Okay, brother. And many people were saying that Prashant Bhaiya only teaches up to 10th grade, where does Prashant Bhaiya teach in 11th grade? Foolish child, there was no time until now, so I didn't teach. Otherwise, I passed 11th and 12th many years ago. Your exam is IIT JEE, I have cleared that exam, JEE Main, JEE Advanced, both. I have also got ranks in it. So, I can teach. But there was no time until now. But now I have come for you, and I will teach in such a way that you will enjoy it. Okay. Let's move on. What is conversion of units? This is very important. Look, son, what will the question be? The question will be, I will tell you similarly. The question will be, I will tell you. Convert, convert, convert 3 meters into CGS system. Convert 3 meters into CGS system. Okay, what is the unit of 3 meters? Meter. Into what do we need to convert? CGS. What was in CGS? Oh, tell me the unit of length. Centimeter. How many centimeters? Now you don't have to write the answer directly. In school, there is a way to solve it. What is the way? Look carefully, son. What is this? We can call this N1, that is, the numerical value. This is the unit. N1 U1 will be equal, whatever system they are in. It's a step-by-step process. It might seem a bit difficult, but understand, it's easy. This is how it has to be solved. Okay. What is N2? And what is U2? U2 is the second type of unit, the second unit. And what is N2? The numerical value. Remember, N1 U1 will be equal to N2 U2. You still don't understand. You will understand from the question. Here, what is N1? Three. What is the unit? Meter. What do we need to find here? We need to find N2. We are given the unit. What is the unit? Centimeter. What is given? Centimeter. We are given the unit. Okay. Now look what I will do. I will convert this meter into centimeters. How? 1 meter is equal to. Oh, say it with me quickly. 100 centimeters. Okay. Now I will write here that 3 * 100 centimeters = N2 * centimeters. Okay. Now look, centimeters and centimeters are cancelled. What is finally obtained? The value of N2 is 300. What is it? 300. What is it, son? 300. That is, in the new system, that is, in the CGS system, now my value is 300. Do you understand? Yes. This is the way we have to solve these questions. This is mandatory. This process is mandatory. Remember, N1 U1 will be equal to N2 U2. That is, even if the system changes, the product of these two things when we multiply them will remain constant. Now I will show you a very unique thing in Maths. You will need to concentrate a bit. Look, what is the concentration? Look, N1 was less here. N1 was less here. And U1 was more here. Because meter is big, centimeter is small. Now what happened finally? Here, look, N2 has become more. Because U2 was less. U2 was less. Understand? Understand? That is, if your unit becomes bigger, your numerical value will become smaller. And if your numerical value increases, your unit will decrease. That is, what I wanted to tell you from this question is that the numerical value is inversely proportional to the unit. And this is a very important point. Remember that this is very important. N is inversely proportional to the unit. Okay. This is very important. Because in many questions, in many papers, I show it directly. Such a question comes directly. What will come? A physical quantity is measured and its value is found to be N U. N is the numerical value, U is the unit. Then which of the following relationships? Oh ho, it talked about relationships, brother. Shit, old memories. No, no, son. Not a joke. We are studying in serious mode now. No jokes. I will teach. Yes. What will be the answer? It will be D. If anyone writes it wrong now, what should I hit you with? Where is my tool? I will now, son, I keep new tools with me. If you children give wrong answers, then I keep this tool of mine. This one. And it has become a little crooked. Straighten it. This nail cutter tool. Be afraid of me a little. Be a little afraid of me. Okay. Let's move on. Let's practice some more questions. But before doing that, you need to understand a table. You must have seen this table somewhere in your lower classes. If you haven't seen it, I will tell you. Look, if somewhere it says 1 Giga, like it says 1 Gigameter. What does it mean? Giga means son, 10 raised to the power 9. So, 1 Gigameter will mean 10 raised to the power 9 meters. Similarly, Mega. We studied it in electricity. Megaampere. What does Mega mean? 10 raised to the power 6. What does Kilo mean? 10 raised to the power 3. Hecto means 10 raised to the power 2. Deca means 10 raised to the power 1. Deci. Deci. That is, we say, one decimeter. So, it means 10 raised to the power -1. Centi. We say, centimeter. What does it mean? 10 raised to the power -2. And Milli. You should also know this. Okay. Apart from this, Micro. What is Micro? Micro means 10 raised to the power -6. For example, if someone says 1 micrometer, what will you write? 10 raised to the power -6 meters. And similarly, nanometer. Nano. 10 raised to the power -9. So, you should know these basics. Sometimes some related questions come from them, so you should remember this table. Let's look at some questions quickly. Look, brother, let's do the first question. What is it? Convert 72 km per hour into CGS system. Look, CGS. Here, the distance is in kilometers. Here, it will be in centimeters. Very good. And here it is in hours. Here it will be in seconds. Now I am going to write the same N1 U1 = N2 U2. Step number one. Step number one. Now look, what is N1? 72. What is U1? Kilometer per hour. Right, son? This is it. Now look, I need to find N2. I need to find the numerical value. What is the unit? The unit is centimeter per second. Because here it is kilometer per hour, so here we will write centimeter per second. This is what we will write. Yes. Now what will we do, son? The same simple method. Convert this kilometer and these hours into centimeters and seconds. That is, tell me one thing. How many meters are there in 1 kilometer? 1000 meters. And how many centimeters are there in 1 meter? 100. So, it is multiplied by 100. Okay. So, now I will write here 72 * this is 1 2 3 4 5 divided by these hours. Divide into seconds. Into what, son? Seconds. 1 hour has 60 minutes, and 1 minute has 60 seconds. That is, it will be 60 * 60. Very good. N2. This centimeter, centimeter per second. From here, the centimeter per second will be cancelled. So, the value of N2 will be this. Solve this once. Solve this quickly and check what your answer is. Shall I solve it for you? Since I have done this much, I will solve it for you. The value of N2 is coming out to be 2000. Is the value of N2 2000 for everyone? Tell me once in the chat. Is the value of N2 2000 for everyone? Very good, very good, very good. Correct. Come on, come on, come on. Such questions come, son. Such questions come. Okay, I am giving you this question as homework. Take a screenshot of it. You will solve this. Okay, very good, very good. By the way, understand one thing. Now, where we are going to study, where we are going to study, is a very important thing. Because now we are going to study the dimension formula. The dimension formula is very important. Why, brother? Look, in today's weddings, you will ask, what is the dimension formula? Look, son, in today's weddings, suppose you like a girl, and you are going to her father's house to ask for her hand. So, the father-in-law will not ask how much you earn, what you do. What will the father-in-law ask? Do you know the dimension formula? You will say yes. Then he will ask, tell me the dimension formula of force. And if you cannot derive it. Okay. That's why it's important. Don't ask its importance. Okay. This is very important. Mark it with a star. What is dimension? Look, basically, there are some symbols which we call dimension symbols. It's very simple. Like, the dimension symbol for length is L. For mass, M. For time, T. What is the symbol for current? There are two symbols for current. Either A or I. What? Either A or I. These are both. What is for temperature? For temperature, there is K. Mainly this K is used. What is next? Amount of substance. We write this as mole or we write mole, or we write it like this, N. And last is luminous intensity. This will not be asked, but still, we write it as cd. Mainly what do we write, son? Cd. This is not asked. These two are also not asked. Remove these two. You should know all of them up to thermodynamic temperature. Okay. Clear? You understood this. What are these? Their dimension symbols. Dimension, what is it, son? Read the definition. You will understand in 1 minute. It's a very simple thing. Look, dimensions of a physical quantity are the powers to which the fundamental quantities must be raised. That is, suppose, suppose I need to find the area. Suppose I need to find the area. How will I write it? Area. Think. How is area calculated? Length * Length. That is, I am multiplying length twice. That is, I will write L2. I will write it like this, son. Why? Because I multiplied L twice. Look, this is the dimension symbol. I multiplied L twice. I put a square. Did I do anything wrong? Okay. I am calculating volume. So, what will I do? L cube. Any problem? Any trouble? Any problem? No. This is how we will derive the dimension formulas for many quantities. That is, we will find them. These dimension formulas are very important. They get stuck in the question paper 1101%. Keep watching. We will derive the dimension formulas one by one. Now, look, there is a format for deriving the dimension formula. Like, I am saying, what will be the dimension formula of area? You will say, Bhaiya, the dimension formula of area was L2, which we derived. You said this. Okay. The two, this two that I put outside, here, three and two, bring it inside. Bring it inside the bracket. Okay. Come on. Like, you are saying, like, you will say, Bhaiya, this is the dimension formula. But this is wrong. Why? Because to write the dimension formula, we always need three things: mass, length, and time. Does it have mass? Does it have length? Does it have time? How will I write it? Look, son. M to the power zero. Because there is no mass. Anything to the power zero makes it gone. Bye-bye. Goodbye. Length to the power two. And time to the power also zero. Because there is no time. There is no time, right? Very simple. There is no time, so 0 2 0. Very good. That is, understand it like this. Understand it like this. This is a matter of giving respect. I could have written it like this, but I thought I should give some respect to Bhaiya. So, how am I writing it? 0 2 0. Understood? Understood? Tell me quickly. Let's solve the questions one by one. Come on. Velocity. What is velocity, son? First of all, whatever question comes, its derived unit should come to your mind. What is the derived unit of velocity? Meter per second. Meter per second. That is, above is length, below is second. Above is length, below is second. Above is length, below is second. Okay. Above and below. What is length? So, I will write L. And time was below. So, if I take time above, what will happen? Time to the power -1. So, length to the power is still one. But time to the power will be -1. Will this come from the fundamental unit? Yes or no? Say. Understood? Understood? Oh, foolish child, how simple it was. I took time above, -1. Basic math. Okay. Let's derive acceleration. First, write the derived unit. Meter per second squared. Very good. Now look, what is below? Second squared. So, what will I write? What will I write? Look, LT - 2. LT - 2. Now, we haven't given them respect. When will we give respect? When we put mass to zero with all of them. That is, if I want to give it respect, how will I write it? M0 L1 T to the power -1. This is respect. Respect has to be given, so it has to be added. Okay. Did everyone understand acceleration? Okay. Now tell me, what will be for force? Derive force. What is force? Force is mass * acceleration. And what is its derived unit? We just told you. What is it? Kg. Kg. Say, do you remember or not? Yes. Kg meter per second squared. Okay. So, we can write. We have mass here. We have length here. But here, time will come reciprocally above, and it will become -2. So, T to the power -2. And this is really very important. Remember something or not, the dimension formula of force. You must remember this. How will you remember it? Repeat with me, son. 1 1 2. 1 1 2. 1 1 2. 1 1 2. It's done, right? Just remember this -2. Okay. If you remember force like this, I guarantee you, don't remember any other. Just remember force. You can derive all dimension formulas yourself. Just remember force. Let's talk further. Momentum. What is momentum? Mass * velocity. Mass. Take the mass. Take the mass. Say, mass is M. What is velocity? We just studied the dimension of velocity. LT - 1. Multiply these two. So, what will come? M1 L1 T to the power -1. Simple. Do it yourself. Power. What is power, son? Power is energy per unit time. Power is energy per. Okay, before doing power, you do this. First, derive the work done for me. Solve the work done first. Okay. Solve the work done. What is work done? Force * displacement. Now look, what did I say? Just remember force. What is force? 1 1 2. Say it, 1 1 2. Just remember -2. Into displacement. What is displacement? L. That's it. Very good. Very good. What came? L2 T to the power -2. Okay, son, son. Add this L. It's important. Lest you forget the formula. What is work done? F * s. That is, displacement. Displacement means length. Is it coming? Coming in hazy memories? No problem. Okay. Very good. This is for work done. Now, suppose I need to find energy. What is energy? Energy is equal to work done. That is, this will be for energy. Understood? Energy and work done are equal. Okay. So, for energy, for work done. Now derive power. What is power? Power is energy by time. Okay. So, you already know energy. Just divide it by time. That is, this will go up. And what will come? M1 L2 T to the power -3. Did you understand or not? Tell me quickly. Is this clear? Understood? Very good. So, there are many such questions that we are going to attempt now. For example, I will add one more question here. Pressure. What is pressure? Pressure is your force by area. So, write its dimension. What did I say? Just remember force. What will you do by remembering force? Say, brother. 1 1 2. Say it, 1 1 2. Just remember -2. Divided by area. What is area? L squared. Okay. Now take this up. If you take something up, it will become minus. It will become minus. So, finally, what will be? M1 L

Power -1 to the power -2. Now don't ask how -1 came. When it goes up, fools, it will become -2. Here it is +1. -2 +1 -1. Should I teach basic math? Should I teach basic math myself? Should I become a math teacher? A physics teacher? Should I become everyone's teacher, right? Okay, okay. Now, you will derive some things yourself and tell me. Let's start. Let's start. Let's start with kinetic energy. Now, understand one thing, son. I know sometimes things will seem difficult to you. Sometimes things will seem hard to you. Do you know what separates an average student from a topper? It's self-confidence. That self-confidence should be within you. The world says you can jump 4 feet. Tell the world, "I can jump 8 feet." You know you can't do it, but that confidence should be there. I'm telling you, this confidence will make you win. It's very important. Confidence. Whenever you feel that questions are not getting solved, have confidence. Say, "No, no, we'll do it, we'll do it." That confidence is very important. Come on, with that confidence, solve this question. Come on. Kinetic energy is 1/2 mv². Right? Now you know this formula, but you already know the dimension of energy. The dimension of energy will be the same as the dimension of work. Whose work? The work. So you know the dimension of work, but now we will derive it from this formula. How? See how we derive it. Ignore this constant. We need to focus on mv². What is m, son? m is mass. Right? Into, what was the formula for velocity, son? Remember it once. The formula for velocity was lt minus. And put a square on it. Close it. Right? When you put a square on it, when you multiply it, remove this. 2 will come here, and this will become minus 2. Right? Now multiply it. So it will become m1 l2 t to the power -2. It came. It came. The dimension of energy will be the same, whether it's kinetic, potential, whatever. The dimension of work done is also the same. What is the dimension of work done, son? It's the same. Okay, let's talk about density. Density is mass by volume. What is it? Mass / volume. What is mass, son? m. What is volume, son? l. What is it? l. Right? Now what will you do? You will take this up. Time is not here, so we will make time zero. Very good, man. What a thing. Right? What a thing. Now you, now you have learned. You have become a lion. A lion. Right? Now the next thing is impulse. What is impulse? You don't need to understand it now. Right? You will understand it later, but the formula for impulse is force * time. What is force? Does everyone remember? What was force? 1 1 -2. 1 -2. Very good. Just multiply it by time. Do it in your mind, yourself. 1 1. And time is -2. Here one time is being multiplied. So how much will it become? Did this thing make sense to everyone? Did this thing make sense to everyone? Tell me quickly. Very good. Very good. Very good, man. What a thing, man. This energy, it motivates me a lot. Let's do more questions too. Don't worry now. Come on, let's look at stress. Which stress? See, you will remember the formula for stress in 2 minutes. You remember the formula for pressure. What was pressure? Force by area. The stress is also the same. How will you remember? In the exam, you get stressed, or you feel pressure. Both come at the same time. Exam pressure, exam stress. So the formula for stress will be the same as the formula for pressure. But we have already derived the dimension formula for pressure, right? Very good. Let's look at the next one. Strain. Now strain is very important. Why? Strain has a formula. You don't need to study it now. It will be useful later. Don't understand the meaning of these formulas. Just remember the formulas. What is strain? Change in length divided by original length. Okay, tell me this. If there is a change in length, its unit will still be meters, right? And here is the length, its unit will also be meters. That is, meters will cancel meters. So can I say that the dimensions of this strain will be zero? And we call these quantities dimensionless quantities. I will write its formula. How will I write it? m0 l0 t0. And this is a dimensionless quantity. Very important. Many questions have come on this. Is it a dimensionless quantity or not? Quantity. Okay, next is the coefficient of elasticity. It's nothing. Remember the formula. Stress by strain. Strain is dimensionless. Forget strain. Say bye-bye to it. We know the formula for stress. What is stress? Pressure. Force by area. That is, that is, its dimension formula will also be the same as that of pressure. Which is of stress. Very good. Next, come to the gravitational constant. Look, brother, this is very important. Mark a star on this too. Understand this. It is asked again and again. What is the formula? Force = GM1M2. You must have read this. You must have read this in ninth grade. In ninth grade, I know you didn't study, but you remember the formula, you foolish child. Yes, I remember. Okay, now I have to find its dimension. How will I find it? First, I will write the dimension of force. 1 1 - 2. Very simple, right? G, I have to find. m * m * m will become m². What is below? Radius squared. Radius is also length, right? So I will write l² here. Now I have to find this. So what will I do? I will take this to the other side and bring this to the denominator. Right? When I take this to the multiplication, it will become m1 l3 t to the power -2 divided by m to the power -2. This is the value of G. Now, solve this, brother. What do you have to do? Take this up. It will come in minus. So the final will be m to the power -1, l to the power 3, t to the power -2. This is your final. What? Very good. Gravitational constant. m to the power -1. l to the power. What was it? l to the power, it was 1 minute. Was it correct? Yes. l to the power, our power was 3. t to the power -2. Now it shines. Now it's fun. Very good. You will see many such questions. Now, in this, the more questions you do, son, the fewer questions you do. For example, there is a formula for surface tension. The formula for surface tension is force by length. Now, do you remember force? 1 - 2. What is length? Divide by l. Will you do it yourself? Will you do all the questions yourself? They are not for me to do. Come on, let's look at some more important questions. And this question comes again and again in the paper, and children make mistakes, which is Planck's constant. Now people don't even know what Planck's constant is. Understand the formula, son. There is a formula: Energy equals Planck's constant. This is h. And what you are seeing, you know what it is? It is frequency. What is it? Frequency. You studied this in ninth grade, in the sound chapter. Frequency. Now see, son. E = h nu. This is frequency. If I have to find its dimension, I have to take it to the other side. That is, h = e / nu. Now tell me, what was the dimension of energy? Do you remember? No, you don't remember. Force? Okay, work and energy dimension are the same. Yes, brother. I remember the force. Can I find work? How? What was work? Remember. Work was force * displacement. That is, what will I do? m1. What was force? m1 l1 -2. Now one l will be multiplied here. Right? This is the work. Now, the dimension of energy will be the same as that of work. But the problem is, what is the dimension of frequency? See, son. There was a formula for frequency in ninth grade. If you haven't studied, then remember it now. Frequency is equal to 1 / time period. Whose? 1 / time period. That is, the dimension formula of frequency will be t to the power -1. This is the dimension formula of frequency. Those who haven't studied, remember it. Right? Okay, son. Now what? Now there is nothing. You have to find the value of h. We have e. What is e? 1 l2 t to the power -2 / t to the power -1. Now what will you do, son? Now what will you do? You will take this up. So it will change from negative to positive. Yes. Above -2. From below +1. How much will it become? It canceled out, right? It canceled out. Very good. Very good, man. How much did it become? Oh, add 1, foolish child. Very good. This is your Planck's constant. This is your Planck's constant. Is this point clear? Is the point clear? Tell me quickly. Tell me quickly. Very good. Let's look at the next one. Universal gas constant R. Now understand, son. This is also a formula. You might not have studied it yet. PV = NRT. We have to find this R. Whose? This R. Right, son? We have to find this R. Okay, son. Now try to understand here. What is P? It is pressure. What is V? Volume. What is N? N is nothing. N is a constant. When finding the dimension formula, we forget the constant. And what is T? It is temperature. So write, brother. Write the dimension formula of pressure. You should remember. What is pressure? Then you forgot again. What, brother? Force by area. You remember the force. So derive it. Or else, turn the pages. What do you do? Turn the pages. Right? Okay, brother. Turn the pages. You just wrote them. Don't make so many mistakes. Give me some respite, man. So many mistakes. Right? Okay, brother. What will be the volume? Tell me. l. It will be, right? What is this value equal to? R, which we have to find. We have to find R. And what is T, son? Tell me. Not time. Temperature. How did we write temperature? k. Told you at the beginning. Right? Okay, son. So bring this k here. So this final will come. m1 l to the power 2 t to the power -2 and k to the power also -1. This is your dimension formula. Understood? Didn't understand? Go back a bit. Rewind the video and then understand. Understood? What did we find? We found R from PV = NRT. Okay, don't chase the formula. Right? If you chase the formula, your life will be ruined. What will happen, son? Ruined. I am giving you some questions to practice. For example, you will be able to answer this one. Which of the following quantities is dimensionless? Tell me. Pressure? Strain. What was strain? Change in length divided by length. Yes, brother. Strain is dimensionless. That is, option B. Let's look at the next one. You have to do this question yourself. What is it? Force is given by f = mv² / r. Find the dimension of f. That is, you have to find the dimension with the help of this formula. Brother, I remember the dimension. Oh, I know you remember the force. But you have to derive it from this formula. Like you know the dimension of mass. You know the dimension of velocity. What is r? Radius. What is radius? Length. Derive it. This is your homework. Solve it yourself. Come on, son. Now let's move to the next topic, which is dimensionless quantities. Okay, let's study dimensionless quantities. But before that, solve all these questions. Solve the homework questions. Otherwise, remember my line. What is the line? Potatoes in potatoes, potatoes in potatoes. Sweets in the fridge. If you don't do questions and don't study, you will be beaten. Right? I can hit you by entering the camera, son. You think I'm online, so you're taking it lightly? Are you joking with me? Come on. Dimensionless quantities. I have already told you. Those quantities whose dimension is zero. m 0 l 0 t0. I have already told you. Now you have to remember some dimensionless quantities. Right? What if someone asks you casually? Who knows, brother? What if your father-in-law asks you? Who knows, brother? Anything can happen. Right? Friends. Come on, see. Like the first one is strain. I have already told you. Next is refractive index. Refractive index, son, you studied it in 10th grade. What was it? Speed of light in air divided by in that medium. So both are speeds. Speed cancels speed. Right, son? So this is also dimensionless. Next is Poisson's ratio. What is Poisson's ratio? You don't need to understand it now, but it is also dimensionless. Next is relative density. What is relative density? You don't need to understand it either, but it is also dimensionless. You have to remember this much. Apart from this, some quantities like pi. Pi, right? Pi. Right? This pi is also dimensionless. It has no dimension. Right? Apart from this, some numbers that you will study in chemistry. Like there is a number called Avogadro's number. What is Avogadro's number? Which is 6.022 * 10 to the power 23. This whole number is also dimensionless. So there are some small things like this that are dimensionless. You have to remember this much. You have to remember it, son. Now let's move on quickly. Come on, brother. Now a very important concept is coming, which is your Principle of Homogeneity. This is very important, son. Understand carefully. Why? Because a question can definitely be formed from here in your paper. Brother, see, this is the first chapter. Show some excitement. Solve all the questions. You will finish the questions from all the books. See, what is the Principle of Homogeneity? I will explain with an example. Suppose I give you homework: Rahul, son, Rahul, son, 10 kg + 10 kg equals how much? What will you say? You will say, "Brother, are you crazy? Are you asking childish questions? Everyone knows it's 20 kg." Right? But first, I will slap you for calling me crazy, and then I will ask you a question. Now tell me, 10 kg + 10 cm equals how much? Tell me. If someone wrote 20, I will bring dumbbells and return. Right? Tell me. They can't be added, right? Why? Because their units are not the same, right, brother? So can I say that I can only add things whose units are the same? Yes. Is this thing allowed in subtraction? Absolutely. Tell me, can you subtract 10 cm from 10 kg? How will you do it? How will you do it? You can't, right? Why? Because here too, the units are different. So can I say that we can only subtract and add in the same units? Exactly. This is the Principle of Homogeneity. What is the Principle of Homogeneity saying? The Principle of Homogeneity of a dimension states that an equation is dimensionally correct. Dimensionally correct only if the dimensions of each term on both sides are dimensionally the same. I will explain. Don't get confused. First, remember these words, because they are asked in the paper. What does it mean? Suppose I added something. 10 kg + 10 kg equals how much? 20 kg. Now, in this equation, the units of all three things must be the same. That is, this will be the same, this will be the same, this will be the same. It's not like 10 kg + 10 kg = 20 cm. You can't write that. Units must be the same. That is the main thing. That is, the Principle of Homogeneity says that if you add, subtract, your units must be the same. Now, suppose there is an equation. Suppose there is an equation a + b = c. The dimensions of a. See, units are dimensions. You understood what I said? Units will be the same. Units can be called dimensions. So can I say that its dimension will be equal to its dimension, and the dimension of both will be equal to this also? Can I say that the dimensions of all three will be the same? Yes or no? Yes or no, son? Absolutely, I can say. Now let's come to some examples. Some examples we have. Like you read an equation of motion in class ninth. v = u + at. Did everyone read this? Yes. Did you read this? Can I say from this equation that its dimension will be equal to its dimension, and the same will be equal to this also? You will say, "Absolutely." Let's prove it. How? Write velocity. Dimension. Oh, foolish child. What is this? Initial velocity. Its dimension will also be the same. lt -1. And acceleration * time. Write its dimension. So see, what is acceleration? Acceleration is lt -2. We are multiplying it by what? We are multiplying it by time. By what are we multiplying? By time. When you multiply, the final answer will be what? lt -1. Which is equal to both of these. That is, the Principle of Homogeneity is proved. That yes, it is dimensionally correct. It is dimensionally correct. So such questions come. They will give you some equation and ask you to prove that it is dimensionally correct. So what will you do? You will find its dimension formula. You will equate it to this, and then equate it to this. Simple. Let's do some questions, and you will get more clarity and become stronger. Come on, son. Let's solve some questions, son. What are you saying? Come on, let's solve questions. What is it? Using dimensional analysis, check the correctness of the following equations. You have to check and tell whether these equations are correct or not. Right? Which of these equations do you find correct? Tell me by checking once quickly. By checking, tell me. Like, like I will check this one. Right? s = ut + 1/2 at². Does this equation tell us that the dimension of s will be equal to this, and the same will be equal to this? Is that what it's telling? So, come on, son. The dimension of s is l. Just l. Displacement. Simple l, right? m0 t0. Forget it. u * t. What is u * t? Okay, u is l1. And and t to the power -1. Right? And we are multiplying by t. That is, multiplying by time. So, here too, it will become t zero. So this also became equal to l. Very good. Now let's look at this. 1/2 at². See, forget the constants, like you forgot them, son. Forget the constants in the same way. Right? Okay. At². Now, you know the unit of acceleration, which is. Tell me. Very good. And here is t². So these two will be multiplied. So it will become zero. That is, here too, it became l. That is, this is dimensionally correct. This is dimensionally correct. So, you have to check the dimensional correctness of other questions in the same way. You will check its this, this will be equal to this, and this will be equal to this. These are very important things. Right? You can check them yourself. There is no sense in doing too many questions of the same type. Let's move to the next type of question, which is on your screen. Come on, son. The question worth 1 crore will come, son. Solve it quickly and tell me. Come on, quickly. Could anyone solve it? Okay, you, like this.

I don't think the 11th class is ever that different from the 10th, is it? That's why I say, remember one thing: a 10th mark sheet and 10th love never come in handy in life. Okay? Both have zero value, understand? Yes, very good. Now you've come to 11th, right? Now you must have realized the truth of life. Let's see. Let us consider an equation, 1/2 mv² = mgh, right? What is it saying? Check whether this equation is dimensionally correct. Look, forget the constants. It's m and v². Right? What is v²? lt⁻¹. What should I do with it? I'll square it. Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? I squared it. Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will be equal to its dimension, and that will be equal to its dimension. Good. What is this? Distance. So, what is the dimension of distance? Come on, say it! What is it? Is it this? Will this be equal to a, which we need to find, multiplied by this? What is t? Time. Very good. And will this be equal to b, which we need to find, multiplied by what is here? t². Tell me, will all three things be equal? Quickly look and tell me. Will all three things be equal to us? Absolutely equal, brother. There's no need to think about this. Okay? Now we will find the dimensions of both a and b. Look, first of all, take this t here. So, the dimension of a will be how much? lt⁻¹. This is for a. Good. What about b? Let's see, my dear. b is equal to l. So, bring this t here. So, the dimension of B will be, look how much it will be: l T⁻². This is the dimension. Now tell its unit. What is l? Length. In what is length counted? Meter or kilometer, whatever is given in the question. Here, we are given kilometer. I said, okay. And this is the square of time. So, can we say kilometer per second square? Can we say this? Absolutely. So, your answer for B has come. Right? So, by finding the dimension, the unit also becomes clear. Okay, dear? Okay, dear? Okay, dear? Is this understandable to you fools? It's not like it's going over your head. You can try one question of this yourself, right? I mean, there are many questions like this, but these are enough. Questions beyond this don't come in the paper. Absolutely. Now let's move to the next topic, which is considered the toughest topic of this chapter. But why to fear when Prashant Bhaiya is here? I am here, right? I'll take care of it. Look, what is the name of the tough topic? The name of the tough topic is Applications of Dimensional Analysis. Until now, what we were doing, we call this process Dimensional Analysis, that we check dimensions on both sides, right? It has a very big application in which very tough questions come. I'll do it. Its name is Deriving Formula, meaning we can derive any formula. Really? Yes, we can. Not the entire formula, but we can derive it. How? Let's take an example, brother. What's the example? In the question, it will be given like this: Derive the formula for the time period of the simple pendulum. Find the time period of the pendulum. Pendulum hangs like this, hangs, hangs, hangs. Yes, find the time period of the pendulum. And what is given to us in the question is that the time period depends on what things. Look, my dear, it is given to us in the question that the time period of the pendulum depends on two things. First thing: Length. How long is the length? Second: Acceleration due to gravity. Now I am telling you the step-by-step process. It will be a little tough, but it will be fun. Look, what to do? We know that the time period is related to what two things? g and l. But we don't know what the power of g will be, what the power of l will be. Is it directly proportional? Inversely proportional? So, what do we say? t is directly proportional to l raised to the power x, I assumed. And g raised to the power y, I assumed. I assumed the power, right? Okay? This should be equal to what? mgh. What is m? Mass. Good. What is g? Acceleration due to gravity. So, whatever acceleration is, that's g, i.e., l²t⁻². Right? lt⁻² and what is h? Height. Height means length. Alright, let's check this. So, this will come out to be what? m¹l²t⁻². Will this be equal? Let's see. Here, m¹ has come. Multiplication has happened. l² and t⁻². Have both these things become equal, my dear? Absolutely equal. This means it is dimensionally correct. Understood, right? Nothing new. This is how we check if something is dimensionally correct, my dear. And there's nothing new in this. For example, I'll show you this question. This is a very good question, my dear. Look at it carefully. What is it saying? If x = Oh oh, talk of x again. x = at + bt². What is it saying? x = at + bt², right? In which x is distance. I said, very good. And t is time. I said, very good. So, it is asking you to tell the unit of B. Tell the unit of B. Now understand, its dimension will

You will do it if it is even, you will leave it as it is if it is odd, okay, same, meaning, now look, what is in this, it is odd, right? The digit before this is three, three, what will you do with three? You will add +1. If it were four here, what would you do? What would you do? You would remove this five, nothing else. It would become 64.64, just understood? Let's do it with some questions, come on, let's round off. Let's round off the following into three significant figures. You have to do it up to three significant figures. Where is the third significant figure? 1, 2, 3. What will you do? You will look at the next value. You will look at this. It is four. Is it less or not? It is less, right? So, you will just forget these and write these, 1, 2, 3. Just the answer has come, understood? Let's see another one. Well, how many significant figures are there in this? These three are not there, right? There are 1, 2, 3, 4. Which is the third significant figure? This is it. You will look at the thing after this. It is six. It is more than five, so what will you do? You will add +1. So, this will become 0.098. Okay, understood? Look at this. 1, 2, 3. The fourth one. What is the fourth one? Tell me, man, what is the fourth one? It is greater than five, so what will you do? You will add +1 to this, right? When you add +1, what will this become? When you add +1 to this, look, 1, 2, 3. This was your third significant figure. Now what will you look at? You will look at the one after this. It is greater than five, so it means you will add +1 to the previous one. If you add +1, it becomes zero, one is carried over here, another zero here, right? Then one is carried over. So, this has become 6.00. What has become? 6.00. Okay, 6.00. So, there are many such questions to calculate significant figures, right? You understood rounding off, right? No problem? Let's do one more question. 1.35. Round this off within significant figures. First, second. What is the next one? Five. Now what will you look at? Is the previous number odd or even? It is odd, brother. What did we do with odd? We added +1. Did it click? Now you must have understood. Let's move on. Your next topic is operations, brother. You are going to become a doctor. Oh, not those operations, brother. Not those operations. Now we will do operations of significant figures. Meaning, suppose you have to do addition, subtraction. They have a rule. Multiplication and division have a rule. Let's understand with examples. Look, whenever we are adding something, we have to keep the decimal in mind. For example, this is the rule, son. For example, suppose you have to add this. Add it. How do you add it? Like you have to add, either it will be 12.11, add 0.3, and put zeros ahead. If you add, it will become how much? One. This will become four. This will become two. This will become one. So, 1, 12.41. This has become your. This has come, right? 12.41. Is this the correct answer? No, no, this is wrong because in significant figures, we have to add differently. Yes, this is a different kind of addition. Do you know what the rule is? The rule is, you will look at the minimum decimal places of the things you have added. The things you have added. What are their minimum decimal places? Like, I have added this. How many people were there after the decimal? Two people, two digits. How many were there here? One. What is the minimum, brother? The minimum is one. So, it means we have to round off the answer and bring it to one digit. How will you do it? You will look at this one. You will say, one is less than five, right? So, forget this one. So, this has become 12.4. Did you understand? It is the same in subtraction, same in addition. What are we doing, son? We are doing nothing. We are doing a very simple thing. What? Say it, man. We are looking at the least decimal. I will do one more question, it will become clear to you. 5.33 + 2.32. Add it. How will you add it, son? Tell me, what will come? Add them once. 7.7.653. This is coming. But is this answer correct? No. What are the minimum decimal places? The minimum decimal places were two here. How many are here? Three. So, it has to be converted to two. How will you do it? You will look at this. Oh, this is less than five. So, come back. Okay, brother. 7.65. Is the answer correct now? Absolutely correct. Whether it is addition or subtraction, it has to be done like this. Clarify this thing. Now let's talk about multiplication. The rule for multiplication is a bit different. For example, in multiplication, what do we have to do? I will give you an example. Like 1.1.02. 1.02 * into uh, with what should I multiply? I will multiply with one itself. Okay, I will do it with one itself. What will be the answer? You will say, brother, the answer will be 1.02. But is this answer correct? There is a different method for multiplication and division, son. Understand. We don't look at decimals here. What will we look at here? We will look at the minimum significant figures in the two things that were multiplied or divided. How many were there in this? Three. How many were there in this? One. So, the answer has to be written in the minimum significant figures. Meaning, I have to write my answer within one significant figure. How will you write it? You looked at two here. You saw that two has no meaning. So, you wrote 1.0. Now how many significant figures are there? Two. Two, right? Now what will you do? You will forget this zero as well. This will become your one. So, this is your. This is your final answer. Understood the point? How in multiplication, what are we doing? In multiplication, we are looking at minimum significant figures. This is very important. In both multiplication and division. Let's do some questions, you will understand. Come on, like suppose I have to add these three things. Add these three things once and tell me, son, how much is it coming? Quickly. How much will it be? Add these three things once, quickly. How much will it be? It will be coming as 31.3123. This will be coming after adding all three. This is what you added. Now, is this answer correct? No. What is the minimum decimal place? Here it was two. Here it was one. So, it has to be brought to one decimal place. How will you do it? You will look at this. Oh, it is less than five. Remove it. It is less than five. Remove it. So, this has become 31.1. Understood? Now let's see a multiplication. Look, if I have to multiply these two things. I will not use a calculator. So, I have written the answer below. When I multiplied these two, the answer came as 8.55. Yours must have also come. But is the answer correct? No. How? What are the minimum significant figures? Here it is two. And here it is three. So, in how many do we have to write the answer, son? In two. But this is in three. So, what will I do? Here is five. Oh, if there is five behind five, and there is an odd number behind it, then what do I do? I add +1. So, how much will the answer come? 8.6. Did it click? Did it click or not? What do we do in multiplication and division, son? Did you understand this point? Did you understand this point? Let's do one more multiplication question, it will give more clarity. Look, express the result of 0.0. Such. This is your value. We are multiplying this. We did the multiplication. The final answer came. Is this answer correct? What are the minimum significant figures? Look, how many will be here? Forget these. 1, 2, 3. There are three here. And there are two here. In how many will we write? In two. The answer, I have to write it within two significant figures. Look at the answer, right? Will you count these two? No. This will be the first significant figure. This will be the second. Right? You have to write it within two. So, now I will look at the previous one. What is the number? Five. Now I will come back. It is an even number, so nothing to do. Write the answer. 0.026. This has come your answer within two significant figures. Is the point understood? Yes, it might seem a bit complicated. But question practice is essential. This is what I am saying. And don't give up. You give up so quickly. It's no fun. Because I know you can do it. You have the passion. You can do it. Okay, here is another question. You will try this. This is your homework question. Look at it once quickly. Looked at it. Inside this also, look, what is there? The side of each is given. And you have been told to tell the total surface area and volume. How do we find the volume? We have to multiply all three sides. Right? If you multiply, the answer will come. But remember, what are the minimum significant figures here? 1, 2, 3, 4. So, you have to write the answer within four significant figures. Write it quickly and tell me in the comments. Okay, is it clear up to here? Let's move on. Right? Now comes our next topic, which is a very basic topic. But because it is asked in school exams, I will not teach it in detail. I will go over it briefly. Then we will move towards error. Error is a very important topic. A very interesting topic. Last year, error was removed from NCERT. But this year, error is in NCERT. So, questions can definitely be asked from it. Okay? What is least count? Least count is a very simple thing. What is the minimum data that we can calculate from any instrument? That is called least count. Meaning, least count is the smallest measurement that an instrument can provide with accuracy. For example, you must have seen a scale. Have you seen a scale? How is the numbering on a scale? 1 cm, 2 cm, like this? But within that 1 cm, there are also 10 lines. Have you seen? 10 lines. Have you seen? Yes. So, the minimum our scale can know. Do you know how much it can count? 1 cm divided by 10. Meaning 1 mm. Meaning, if I tell you the least count of my scale, it will be 1 mm. So, what is least count? That your instrument can calculate the minimum value. That's it. Simple. Understood? Clicked? Look at the scale. There were 10 lines within 1 centimeter. 10 lines. Meaning, I can calculate a minimum of 1 mm. Right? Now, two-three instruments come here. One instrument is your screw gauge. I know it hasn't been shown in your school. Mainly in schools. I know the condition of schools. But yes, if it is not being shown somewhere, ask the teacher. Sir, what is this screw gauge? What is a vernier caliper? Ask. Okay. We won't go into detail now. For now, just understand a diagram. Just understand how a screw gauge looks. In a screw gauge, there are two things. I will explain to you. Right? Look, the first thing is your circular scale. This is a round scale. And this is your main scale. Two scales. Circular scale, main scale. Circular scale, main scale. Okay? Now, your instrument looks like this. Where does the question come from? The question comes from telling its least count. So, there is a formula that you must remember. What is it? The formula for least count is, son, remember what? The formula for least count is very important. It is asked repeatedly in schools, and they don't even teach it in school, yet they ask. The formula for least count is, in its case, pitch divided by the number of divisions on the circular scale. Now you will ask, brother, what is pitch? We watch IPL, we don't watch that pitch. That pitch. Wait, I will tell you. Number of divisions on the circular scale. What is this? In that circular scale, how many divisions are there? So, in your instrument, there are 100 divisions, son. Mainly, how many are there? 100 divisions. So, the formula will be pitch divided by 100. Okay? But brother, what is pitch? Tell me that. How will I find pitch? If a question comes? Look, there is also a very basic formula for pitch. What is it? Pitch is the distance moved by the screw divided by the number of rotations. Meaning, when I rotate it, that thing moves forward. So, how many times did I rotate it, and how much distance did it move? Suppose it moved 1 cm, and I rotated it 10 times. So, what is the pitch? The pitch has become your, son, 0.1 cm. Pitch has become 0.1 cm. And what is the formula for least count? The formula for least count is pitch by number of turns, which is 100. Okay? So, in this way, sometimes questions come. Questions come like this. Look, in the question, the pitch will be given. That the pitch is this much. And there are 100 divisions on the circular scale. So, tell me, what is the least count? So, what will you do? Nothing. You will divide the pitch. Yes. You will divide the pitch by the number of. Okay? So, it will be 1 mm / 100, which will be how much? 0.01 mm. In this way, we find the least count. Now, there is another thing, vernier caliper. You don't need to understand it in that much detail. But yes, vernier caliper is also an instrument with which we measure the distance of something. Now, vernier caliper also has a least count. For the least count, the formula will be the same, son. What is the minimum distance? Now, I will give you a formula for this. It's a slightly awkward formula. I would say there is no need to remember it if you can't remember it. No need. I will show you its diagram. Look, it has two scales. Two scales. One is your main scale, which you can see above. And this is your lower vernier scale. This is the vernier scale. This is an important scale of the vernier caliper. Right? This is one of its scales. So, if you want to find the length of anything. Then there is a formula for it. That is extra knowledge. Don't remember it. What is it? Main scale reading, which is the reading of your main scale. Plus, the reading of your vernier caliper multiplied by the least count. Okay? But this has no use. If this topic is not being taught in your school, it is not taught in 80% of schools. So, don't remember it. Forget it. Okay? But there is a formula here, which I wanted to tell you. Okay? Now, what is least count? What is least count? What is the minimum it can measure? So, usually, the least count of a vernier caliper is 0.1 mm. Up to 0.1 mm, your vernier caliper can accurately measure data. Okay? Clear? Tell me quickly. Done? Done? And if you take out the NCERT book, there is also a question in it. Read this question. Look, what is given in this question? If you look at this question carefully, what is it? A screw gauge of pitch. Look, we are given the pitch, and we are given the number of divisions, and it is asking for the least count. How will you find it? Pitch divided by divisions. So, such questions also come. Such questions also come. Okay? Now, before moving to the next topic, there is a very important thing I want to tell you. Look, whenever we calculate readings of anything, if you do an experiment, the more number of readings we calculate, the more experiments we do, the more accurate the answer will be. Meaning, the more number of readings, the less error there will be. Less error. Error, you understand? Mistakes. Mistakes. You have also made many mistakes, right? Mistakes. So, the more readings we take, the less error there will be. Understand? Understand? The more readings, the less error. Obviously. The more calculations you do, the less error there will be. So, such a question has also been asked in NCERT. What is it? We have to measure some diameter. So, in that, why is a set of 100 measurements of a diameter expected to yield a more reliable solution? Meaning, when we did more experiments, we calculated the diameter 100 times, then why did we get an accurate diameter? Because when we increase the number of experiments, the chances of error decrease. Is this point clear? Done? Now, brother, what is error? Error is mistakes. So, let's start this big disease called error. I know children are afraid of it. But why fear when Prashant Bhaiya is here? Right? Right? So, I will take care of it. You chill. You chill. If you don't have to work this hard. We, what happens is, when you come to this class, new, new. I know somewhere you get a little demotivated. Sometimes things start seeming difficult. But as I have always told you, and I am telling you today as well, smile. Always hide your sorrows from those people. Time will tell who we are. And our time has come. Right? This is your time to prove those people. When the result comes, son, and if your result is good, then relatives and victory is in that. Right? Parents feel proud. That is the moment. We work hard for that moment. Let's see the error. Don't give up. We will fight together. What is error? Very simple formula. The formula for error is true value minus measured value. Let's assume the correct answer of something is 100, and when I calculated, it came as 102. So, what will I say? What is the error? What is the error? True value, which was 100, minus measured value, which was 102. Meaning, the error is -2. You will say this. But this answer is wrong. Remember, in error, we never look at plus or minus. Forget it. You have to write 2. Not +2, not -2. We don't look at it in error. Is it plus or minus 2? What difference does it make? A mistake is a mistake. Plus or minus 2, it doesn't matter. Meaning, what is error? It is your true value minus your measured value. Okay? This is your error. Very basic. Now, there are some formulas for error. Don't go into that much detail. It looks so scary. I will just tell you one by one. Understand the formulas. First formula is. Don't go into that much detail. Just understand. What is absolute error? What is absolute error? What is the formula I told you just now for calculating error? That's it. Absolute error is real value minus what we measured. Right? Like, in a question, suppose I have to find the absolute error. Your real value was 12.5, and what you measured came as 12.3. So, what will be the absolute error? 0.2. Forget plus or minus. Okay? 0.2. This is what has become your absolute error. Very simple. Anyone can find absolute error. The next term is relative error. This is important. The formula for relative error is what? Absolute error divided by true value. Right? What is this mean value? I will tell you. Absolute error divided by true value. For example, let's see in a question. In which, in which, in which, look, your value was 100, and your answer came as 102. First, tell me, what is the absolute error? How much will it come? Don't write -2. I will beat you a lot. What is relative error? It will be absolute error divided by true value. This is what has become, son. This is your relative error. Okay? Now, there is one more thing, percentage error. Percentage error is nothing. We just take the relative error and what do we do?

We multiply by 100, right? Then that becomes the percentage error. For example, 2 / 100 * 100, this gives you 2%. So this is your percentage error, okay? It was very simple. Did you understand relative error? Absolute error divided by true value, the actual value, and the absolute error that came, right? Did you understand this? I have also told you about percentage error. What is percentage error? What is the formula for percentage error? Relative error multiplied by 100, right? Relative error multiplied by 100. So remember, percentage error is also a very simple thing. Is everything clear? Tell me quickly, tell me quickly. Very good. Relative error * 100. If you remember these three formulas, you can solve any problem in the world. Just like I showed you. But the problems are not that easy. What kind of problems come? Now I will show you. Now the fun begins. Now the game starts. Look, I won't waste much time. We will start quickly. Problems come at this level, meaning the true values are not given at all. If, for example, the true value is given, and you know the value you got in the experiment, then anyone can solve it. They can find the absolute error, they can find the relative error too. But what will be given in the problem? Look at this. When we measured the time period of a pendulum, we got five different types of time periods. One was 2.63, one was 2.56, one was 2.42, one was this, and one was this. Now tell me, how will you calculate the absolute error, relative error, and percentage error? Do you know what to do here? This NCERT question is important. When the true value is not given, you have to take the mean and assume it to be the true value. What did I say? When the true value is not given, take the mean and assume it to be the true value. How do we find the mean? We add everything and divide by the number of quantities. For example, how many quantities were there? 2.63, 2.56, 2.42. Add all of these and divide by five. I won't do this calculation now; it will waste time. You try it yourself. So the mean value you get will be this. How much will it be? It will be this. Now, this mean value of yours, this will be the true value. Understood? Now I need to find the absolute error. How will I find it? Not one absolute error will be found, because look, there are five quantities. So I will subtract this from this, this from this, this from this, this from this. So now I will keep subtracting. I did this, I did this, I did this, I did this, I did this, and I got five different absolute errors. But there should be only one absolute error. So, I will take the mean of all of these. How will I find the mean? I will add them all and divide by five. That is, add all, divide by five. Total values are five. So now my final absolute error will come. I will find the final absolute error, and it will be 0.1062, right? It will be this. We won't do this much calculation; time is short, so I have already done it. You try it. Now the absolute error has come. How do we find the relative error? Absolute error, which is this, divided by, divided by, tell me, the true value. In this case, what is the true value? Tell me, tell me, the true value is the mean value. What is the mean value? 2.624. This is your relative error. If someone asks for percentage error, just multiply it by 100, brother. This much calculation is there in these problems. Yes, but such problems are asked very rarely. But they are asked for quite a good number of marks. So you will get good marks in school only if such problems come. Otherwise, such calculation-heavy problems, brother, don't come. Don't take too much load. Okay? So if you solve this, the final percentage error will be this. This was the relative error. Multiply by 100, it became 4.09%. Try solving this. Did you understand my flow? What am I saying? Whenever you are given different readings and the true value is not given, first we will find the true value. How? By taking the mean. What will we do, brother? Mean. The true value has come. Now what will I do? I will subtract everything. I will find the absolute error. Five absolute errors came. Now I will take the mean of these five, and that will be our main error, the main absolute error. Now, how will I find the relative error? Absolute error divided by, tell me, the true value, which was the mean. Simple. Now, I am giving you one such problem to solve. Okay? In this, there are three measurements of length. 1, 2, 3. And here the true value is given, brother. Look, in this problem, the true value is given. So now you, now you don't need to find the mean here because the true value is given. So you can directly find the absolute error. How? First, subtract this from this. Then subtract this from this. And remember, forget negative, positive. To hell with negative, positive. If the answer is negative, you have to write it as positive, right? We don't see that in error. And subtract this from this. Okay? Three absolute errors have come. Now what will you do? You will add all three and divide by three. You will find the mean. So that will give you a main absolute error. When your main absolute error comes, you can find the relative error from it. Then from relative, you can find the percentage. Solve this and tell me which children got the correct answer. It's a very nice problem. Such problems are seen in papers. Okay, let's move on quickly. Rules of error propagation. Come quickly. What are the rules of error propagation? This chapter will end in the next 10 minutes. Understand carefully. What are the rules? If I have to add anything, look, how I write quantities, I will tell you that. How I write the final quantity. Like in this problem, in this problem, our error was this absolute error, right? What was the true value? Our true value came out to be this. If I have to write this quantity, you know how I will write it? 2.624 plus minus. We put this plus minus. Then we write the absolute error. What do we write? Absolute error, which is 0.1072, right? We put this plus minus. This is the way to write error. First, you have to write the true quantity, then plus minus, whatever your absolute error is. Okay? Now what are we going to study? Imagine there are two values, and if we have to add or subtract them, how are we going to do it? There is some rule for it. What is the rule? Errors will always be added. How? I will explain. Suppose one was 10 + - 0.1. This was the first value. We have to add it to 10 + - 0.2. These are two values. We have to add them. How will you do it? You will add these two, and you will also add the errors. How much did it come? It came. Simple. Just add. What will happen in subtraction? Let's see. Suppose, suppose we have to subtract them. Now tell me, what will happen? You will subtract 10 from 10. How much will it be, brother? Zero. But remember, whether it is addition or subtraction, errors are never subtracted. Errors are always added. Errors are always added. So you have to add these two. Plus minus 0.3. So if I subtracted, what was the answer? So mine came out to be this. Did you understand? Did you understand? That is, whenever I have to find the error, whether it is subtraction or addition, I will always add the errors. I can subtract these things, but don't mess with the error, brother. Let's move on. Let's see some problems. Like, suppose, like, suppose we have to add them, or we have to subtract them. How will you do it? You will add these three and add these as well. Right? Now, suppose calculate the difference between A and B. That is, suppose you have to find the difference between A and B. That is, if you have to do A - B, tell me what the answer will be. Tell me what it will be. Subtract this from this. So this will be 15. Plus minus. Remember, errors are always added. Very good. It was simple. Errors are added. There is nothing new here. Now let's come to a very important topic: multiplication and division. Remember one formula, brother. You will have to remember this formula. In NCERT, this is not even there, but it is asked in schools. Remember this formula, brother. What is this, brother? What is this? Whether it is multiplication or division, remember this formula. Why? Why are we doing this, brother? Remember, tell me. I am telling you. Don't you trust me, man? Look, suppose, suppose, look at this formula carefully. It is important. Suppose you have to multiply two quantities. 2 + - 0.1 * 3 + - 0.2. Now how will these be multiplied? One way is, look, it's a normal thing. You will multiply these two. That will be six. But the problem comes in finding the error. Do you have to multiply the error? No. What do you have to do? Imagine, imagine when we multiplied these two, when we multiplied these two, the answer came out to be Z + - Delta Z. What does this Delta mean? Error. Error. Okay? This answer came out to be Z + - Delta Z. Imagine, imagine, we know Z. What will it be? What will Z be? Multiply these two. So Z will be six. That we know. What don't we know, brother? What will the error be? Oh, what will this error be? Now there is a formula for this. What is the formula? Delta Z / Z = Delta A / A + Delta B / B. Delta Z is what we have to find. Delta A is the error in A. What is the error in A? 0.1. Delta B is 0.2. Now, according to this formula, if we write it, then Delta Z, which we have to find. We know the value of Z. How much is it? Six. Right? 3 * 2 = 6. We know the value of Z. How much is Delta A, brother? Delta A is 0.1. And what is A, brother? A is 2. A is 2. Right? Plus, look, there is a plus sign here. Delta B / B. Delta B, Delta B, Delta B. Right? Okay. This is your answer. Now from this, you can find this Delta Z. How can you find it? Oh, fools, solve it once. Solve it once. How much will this be? Solve this once. How much will it be? 0.05 + solve this. How much will this be? 0.1. Tell me quickly, man. You are not even doing this much for me, man. You can do this much, right? How much is it coming? 0.06, right? If you add these, it will be 0.11. Right? Six will go into multiplication here. So the value of Delta Z will be how much, brother? 0.66. How much? 0.66. Now, how will I write the final value? Tell me. How will I write the final value? Tell me. How do I write the final value? Z + - Delta Z. So I knew Z. It was 6 + - 0. Oh, what happened, brother? Oh, what happened? 0.66, brother. Now, did it make sense or not, you foolish child? Did it make sense or not? Solve the problem. Whether it is multiplication or division, this formula should be in your mind. What is the formula? Repeat with me: Delta Z / Z = Delta X / X + Delta Y / Y. Okay? Whether it is addition, subtraction, multiplication, if you have to find the error in the final answer, you have to do it with this formula. For example, here is a problem in front of you. What is it? A student measures the length of the road as L = 50 + - 0.5. Width is given. What is the total area? How will I find the total area? When I multiply. Now, for this formula, what will Z be? Tell me. Multiply these two. 50 * how much? 50 * how much? 10. So Z will be 500. Right? What do we have to find? We have to find the error. Are all things given, brother? Write it yourself. Delta Z, we have to find. I just found the value of Z by multiplying the two: 500. Okay, what is Delta X? What is the error? It is given: 0.5. What is the value of X? X is 50. What is Delta Y? What is Delta Y? 0.2. And what is the value of Y? How much is the value of Y, brother? 10, right? Okay, okay. From this, I will find this Delta Z. And Delta Z, you will find it yourself. And finally, you will write the answer as Z + - Delta Z. That is, your answer will be this. You can see below: 500 + - 15. This should be your answer, brother. Try it once. Try it once. This will be your final answer. Done, brother? Done. Such problems come. Whether it is multiplication or division, you will have many such problems. For example, for example, I will give you one question as homework. I will also give you one for homework. Try this question. Try it. It's a slightly tough type of question. Try it. Okay, on resistance. You can try this. Let's move on. Now, one last topic of this chapter, which is quantity raised to a power. That is, understand. It's a very nice topic, a very small and cute topic. Suppose, suppose I have to find the volume. Right? What is the formula for volume? Tell me what it is. Side cubed. Oh, what is the formula for the volume of a cube? Side cubed. Yes. Now, suppose the value of the side was 10 + - 0.1. Right? So what will the volume be? Look, you can find this by multiplying three times. That is, you can find the value of Z, which will be 10 * 10 * 10, which will be 1000. But can you find Delta Z? Multiplying three things. Look, it's a cube, right? So there is a formula for this, brother. A formula. What is the formula? If any quantity is raised to a power, then if I have to find Delta Z, then Delta Z / Z = 2. This power, it will come in multiplication. Just power * Delta A / A. That is, that is, if I had to find it in this problem, then Delta Z / Z. How much is the value of Z? It came out to be 1000. Equals to, equals to. What was the side? Tell me. What was Delta? 0.1 divided by 10. And what was the power? The power was three. That is, this power will come in multiplication. That's all. From this, you will find Delta Z. Understood? So this is the formula. When there is a power, the power comes in multiplication. There are some simple, simple problems for this. Like, calculate the area of the square. There are two ways to calculate the area. Either you multiply them twice. Side * side. You can do it with the multiplication method. But it will take more calculation. What is the simple method? Tell me, brother. Delta Z / Z = how much power is there? The power here will be two. Into Delta X / X. Can you understand this question? Tell me quickly in the chat. Can you understand the question, brother? Is it entering your brain? Is it entering your mind? Is there no fire coming out of your brain? Are you not becoming like that character from Pakyon who had four heads? Are you not becoming like Charizard? Is smoke not coming out of your mouth? Nothing like that, right? Things can be tough, but they are interesting. Right? So what did I do? If I have to square any value, like area is side squared, right? Side squared. So to find the error, I will bring this two here in multiplication, brother. Nice thing, right? Okay, you can find the answer to this. It's very simple. Now I am going to do one final question for you. Today's last question. The percentage error in the measurement of mass and velocity of the body are 3% and 4%. That is, it says the percentage error in mass is how much? 3%. And the error in velocity is 4%. Now you have to tell me, what will be the percentage error in calculating kinetic energy? What is the formula for kinetic energy? 1/2 mv². Tell me, brother, what to do? What to do? What to do? Just tell me the error. Just tell me the error. Look, when we tell the error, forget this constant value. Okay? Here it is mv². mv². Right? When two things are multiplied, brother, errors are added. Whether they are divided, they are still added. We know that the error in mass is how much? Tell me its error. Its error is given as 3%. The error in velocity, we know it is 4%. How much is given? 4%. Now remember, remember, there is a square here. When there is a square, what will I tell you? When there is a square, this two comes down and goes into multiplication. That is, the error in the square of velocity will be 4 * 2. 4 * 2. So it becomes 8%. The error in M, we know it is 3%. Its error is 8%. So overall it becomes how much? 11%. So 11% error is your answer. Did you understand? We were directly given the errors. Directly the error in mass was given. The error in velocity was given. We knew the formula for kinetic energy: mv². 1/2 mv². The error in M, we know. When two things are multiplied, brother, errors are added. Remember this, brother. Whether they are divided, they are still added. Errors are added. I told you, right? Errors are added. Right? So what is it? Now its error is 3%. The error in V was 4%. But there was a square, so how much did it become? 8%. It became 11%. So these were some of your excellent problems, some fantastic problems. I hope you enjoyed finishing this chapter here. I know the topic of error is a bit tough, but you know what, brother? This is enough for you. Whatever I have done, error will not be asked beyond this. I have taught you a bit of high level. I have taken you to the highest level. I have taken you here. Why? So that your practice continues. That's it. So remember what? That in life, we will keep fighting and keep winning. Here, one chapter of yours ends. But the next chapters will also come. And if you really liked the lecture, enjoyed it, understood it, then definitely put a story on Instagram, tagging me, and tell the world that Prashant Bhaiya has come to teach 11th grade, and now we are going to set 11th grade on fire. Right? Remember. Okay. Our time has come. We will give our best, and we will win too. On this note, thank you everyone. My name is Prashant. See you in the next lecture. Bye-bye.