 Write down is this the last four-hour class or the last morning class? Write down dimensional analysis It could have got it wrong But then even if you get it right you get zero because you have to write Whatever you have in terms of whatever you have measured They're not measuring the time period you're measuring hundred times the time period Okay, but to modify the expression itself So if you divide the error by any constant doesn't just divide normally Like if we did what Vikas said if we did 90 by 100 Then you have to divide the error also then okay So when you divide the error you have essentially increased the accuracy of the instrument Which is absurd you can't divide one from hundred and then say accuracy is now one by hundred Understood accuracy remains one second Whether you measure one time period hundred time period whatever it is All right, but mathematically it may come out to be same answer it may But that will be a wrong method. I can devise a question in such a way that if you do like this will get a wrong answer Okay All right, so dimension analysis, so at the start of the chapter itself we have Assert him or we have found out that there are seven dimensions in this universe It's a no mass length time quantity temperature Luminous intensity and what else? I want a substance Current okay, so if there is a derived quantity all those derived quantities can be written in terms of these dimensions Hmm now these fundamental dimensions now the thing is that suppose Let's say it doesn't make sense to add mass with the length right kg with one meter doesn't make any sense or meter with Time of one second with one meter doesn't make any sense Okay, this you can understand pretty well when I take the example of the basic quantities itself But this is true also for the derived quantities What I'm saying is you can't add velocity with the acceleration one meter per second adding to two meter per second square is Absurd Okay, so when you're adding the two quantities the dimension should match That is when you have that formula v zero to u plus 80 You're multiplying a with t so that meter per second square becomes meter per second Meter per second square multiplying with seconds that become meter per second then you add Okay, so we are going to use this property of universe having seven basic dimensions to Do some analysis and using dimension analysis? You will see that it is it is a very very strong concept Because there cannot be any exception to it. No formula Seven exception of whatever I'm saying that you know you can't add two dimensions Which are different? Okay, similarly when you write force is equal to mass and maturation that equation must be correct dimensionally also Dimension of force should be equal to dimension of mass into dimension of acceleration Are you getting it so when you're equating their dimensions must be equal This is what we are trying to do in the analysis of the dimension Okay, so before we get into the dimension analysis We'll first write down the basic things that are required us to keep in our mind to do the analysis Okay, write it down Okay So an equation Can be dimensionally correct may not be true What do I mean when I say this? The dimensions my dimensions may match. Yeah, but actually that equation has no meaning to it rivers can never happen equation which is Not Dimensionally correct can never be true fine So the implication of this itself is that you write down Two physical quantities cannot be added or subtracted if the dimensions are not same Two physical quantities cannot be added whose dimensions are different Cannot be added or subtracted both, but when we write the dimension of anything Okay, when we write dimension of anything for example, let's say dimension of speed Unit is meter per second The way we write dimension is this We take a square bracket like this Okay, we should write seven dimensions over here Universe has seven dimension But since in our class 11 entire 11th is about more or less mechanics itself mentioned which are defining the mechanics which are what mass length and time only Okay, but it doesn't only three dimension you have to write suppose I bring in You know magnetism or current then you have to use ampere also Okay, but right now. We just need three dimensions Which are mass length and time? Okay, so if you know that the speed is meter and second like this dimension as mass to the power zero It has no dimension of mass Okay length to the power one and time to the power minus one So this is the dimension of this is a dimension of you can you know treat like universe has seven corded access One corded access for mass other corded access for length other coordinates for time like that's seven coordinates are there so caught the speed lies in this L1 t-1 coordinate if something lies Okay, so this is the dimension of speed similarly, you know Simple example speed. I want you to write down dimension of these things. Please write it down. There's things quickly right now Gravitational potential energy K is kinetic energy then I say she will be what dimension? zero L1 t-2 Is a no, what about force dimension of forces Multiply mass with it. It'll be m1 L1 t-2 Candy edges half mv square M1 What about gravity potential energy Mgh Next one is minus one M1 Minus two you can check you know Energy is mg edge So this is dimension of dimension of mg edge is equal to dimension of mass Into dimension of g into dimension of edge Dimension of mass is m dimension of g acceleration LT-2 Dimension of edges L when you multiply it becomes L square fine Okay, now we know that one energy can get converted into another form of energy. We know this or not Okay, so all of the units must be same All the energies have this unit does not matter what kind of energy we are talking about Okay, it doesn't matter Whether it's kind energy potential energy electrostatic energy magnetic energy whatever crap you can think of all has Same dimension all kinds of forces will have the same dimension similarly Because you are adding in subtracting forces Okay, now if I know already if I know that you know if I know that Some variable depends on few little later first let us go slow for example Let's take this one s equal to ut plus half 80 square now Tell me does it make a dimension sense dimension. It doesn't make sense If it is making sense then what should happen Dimension of length should be equal to dimension of what? ut and 80 square dimension should also be ut dimension is length Dimension of a into t square is also length meter per second square into second square if I know that The time period of time it depends with you. I'm trying to say that time period depends Accession due to gravity G Okay, okay now using dimension analysis Can you derive the formula you once I tell you it become very straightforward And come up with the expression time period depends on Length and G Depends on length it could be length to the power eight and G to the power But not like this I mean although you got it correct What if if you don't know it is who tell by G no No, I got this because I wanted to get No, I wanted to get it in terms of Okay, see you can see I want you to do it the way it is Generate because the formula may be very complicated you may not be able to visualize that you know L by G and the root of that is second I mentioned are getting it. There should be generic way to do it Length so let's say T is proportional to length to the power a Also is proportional to let's say G to the power so T should be equal to some constant K times and to the power a G to the power B Understood yes or no Constant has usually no dimension here assuming that this constant has zero dimension Okay, now this is the equation. Can you write a dimensional equation dimension of T is M? 0 L 0 T 1 this is dimension of T This should be equal to dimension of K multiplied by dimension of L to the power a multiplied by dimension of G to the power B K is what nothing So this is dimension of L is L to the power a This is team mine. I am ignoring anything has it having powers 0 So here I have written M to the power 0 to the power 0, but there I have not written M Okay So this is equal to M 0 plus B And T to the power minus 2B So minus 2B should be equal to B will be minus 2B minus 1 by 2 and A should be what? A plus B should be 0 So A should be equal to plus 1 by 2 now come back here T will be equal to minus 1 by 2 so it become T equal to K times root L by G Understood so this method you can use if you know on what physical parameter Your expression should depend on Recreating a force should depend on mass and force should depend on acceleration If you have decided on the dimension of force You'll get the value of an expression how it is That you can find experimentally To derive an expression Okay, so when you put equal to minus half you'll get T is equal to K times L to the power minus half So this will be equal to K under root L by G And experimentally you can find out the value of K is 2 pi There's a question in let's say J advanced or J mains Most probably it will be on dimensional analysis only And good thing it's a straight forward topic So that's it for today Sir, could you give us another one of these questions? I'll give you homework Give me the book Good that you reminded me Homework Book Physics Sentimental All of you have that book, right? Yes sir Yes sir Say how many times do you have to write the book? No, wait, I'll write it Okay All of you please note down See there is a section Page 3.19 Page 3.19 There is a section of J mains It is written J mains Okay, complete that exercise That in a question it will be written as significant figures significant digits So whenever you see that phrase in the question you leave it That will be doing next class Only significant figures we have not done yet Okay, apart from we have done 99% of the chapter So this is stop talking Question number 1 to 40 These are objective question One question will take hardly two minutes So 14 to 2 1 hour 20 minutes So you have one week 168 hours So 1 hour 20 minutes Okay, for J mains And if you are targeting J advanced So that is your target Complete the book So this is book 1 right Yeah, module 1 Module 1 Those who are targeting J advanced Please complete the book Complete module 1 by next Not module 1 book Complete the book as in complete the Chapters Question You can do that Let's see Okay So those who are targeting J advanced There is no limit Even if we have not done significant figures Struggle a little bit That struggle is your learning If you don't struggle If you directly look at the solution All the solution is not available right now It's always me Okay, so if you struggle That is your learning If you are not struggling You are not learning anything Remember that