 Let's solve a question on dimension and analysis. So here we have a question which is that V that is velocity that is equal to under root of AB plus Bt plus C divided by D plus T. And we need to figure out the units of A, B, C and D. So before I go ahead, why don't you pause the video and give this one a try. Alright, now we know that the physical quantities can be added or subtracted only if they have the same dimensions. So if you have velocity on the left-hand side and you have three quantities that are being added, they must have the same units as that of the velocity and the unit of velocity, the unit of velocity is meter per second, right? Velocity is meters per second. So if we write it in the form of dimensions, this will be L that is for meter, T minus 1 because second is in the denominator. Now all of these quantities under root of AB plus Bt plus C, D plus T, all of them individually will also have this particular dimension, right? So with that information, let's try and figure out the units of AB, C and D. Let's pick up the one which has only one unknown physical quantity. So if you pick up Bt, we know that the dimension of T is just capital T and it must, Bt must have the dimensions, it must have the dimensions of LT minus 1, right? And T in itself, T in itself is capital T. So the units of B, the units of B, if we write it in this way, B, this is time, this should be LT minus 1, the units of B, they turn out to be equal to, they should be LT minus 2, right? Only if minus 2 gets added to plus 1, it becomes minus 1. So it becomes T minus 1. Now B is LT minus 2. Now let's go, let's go to, let's go to under root of AB. We know the units of B. We know that this physical quantity under root of AB, it should have a unit of LT minus 1 meter per second. So if B is LT minus 2, let me write that over here. This will be, this will be, let me scroll this slightly. This will be under root of A, which we don't know and this is being multiplied with the dimension of LT minus 2, right? This should be equal to the dimension of LT minus 1, length time minus 1. Now if A has the dimensions of L, then it becomes, then this really becomes under root of L to the power 2 and T to the power minus 2 and when we remove the under root, this will become LT minus 1 equal to the units of the velocity. So dimensions of A, they come out to be equal to just dimensions of length. Now let's look at C divided by D plus T. So for that, for that C divided by D plus T, this should also have the units of LT minus 1, right? And in the denominator, we are adding D to time. So D should also have the same units as that of time, which is as T. So denominator itself has the dimensions of T. You're adding something to, something to time, dimensions of, dimensions of D will also be T. So C should just be length, right? L and therefore C divided by D plus T will really become LT minus 1 because T is in the denominator. All right, so units of A, they are just length. Units of B, they are LT minus 2. C is just L and D is just T.