 All right friends, good morning. So today I'm going to take a question on fluid mechanics. OK. So let's see what this question is all about. Vessel containing water is given a constant acceleration a towards a right along a straight horizontal path. So you can see that there is a direction of acceleration which is given over here, OK? Which of the following diagram represents the surface of the liquid? Now, surface of liquid, will it remain horizontal? Will it incline like this as shown in B? Or it will incline like as shown in C, OK? In order to understand this, you need to first, I think you may remember how we have derived the expression for variation of pressure, right? We imagine a cylinder made up of fluid only, OK? So let's imagine the cylinder over here. So this is a cylinder, OK? This is an imaginary cylinder made up of fluid, OK? This cylinder also accelerates, OK? With acceleration a, all right? Now if pressure over here is P1 and pressure that side is P2, then what I can say that this cylinder has pressure from this side, let's say that pressure is P2. So force will be P2 into a, where a is a area of cross section. And here, the force due to pressure will be P1 into a, OK? So if the mass of this cylinder is m, then I can say that P2a, which is force along right and side, minus P1a will be equal to what? Mass and acceleration, right? So m into a, all right? Now mass can be written in terms of density. So what I'll do, I'll write like this. P1a is equal to density, OK? Into area of cross section multiplied by the length of the cylinder. Length of the cylinder is the volume, length of the cylinder into area is volume, so a into l into a, OK? So what I'll get here is P2 minus P1 is equal to rho a into l, all right? Or I can say that P2 is equal to P1 plus rho a into l, OK? So we have found out something very important. So if the fluid accelerates horizontally, then even the pressure will vary in horizontal direction, OK? So pressure, as you go back side, will increase, all right? Now let's see which of the figure makes sense. So if you say that this is one point and this is another point horizontally, OK? And if they are separated, let's say this is separation by a distance of x, then this point's pressure should be more than that point's pressure, OK? But this point pressure is P2, and this is P1. Then P2 should be equal to P1 plus rho a into x, right? This is what we have derived just now. So if this point pressure is more than that point's pressure, horizontally it is varying. So vertically also it should have come out to be same. So just outside this water, the pressure is atmospheric pressure. So here pressure is same, and there also it is atmospheric pressure. These two points have the same pressure. In order to have this point to gain more pressure, this point should be at a greater depth, isn't it? So this is H2. I can say that P2 should also be equal to atmospheric pressure plus rho g H2, isn't it? And here the pressure will be, if this is H1, pressure there will be P atmosphere plus rho g H1. Now if this pressure is more than that pressure, naturally H2 should be more than H1, OK? So that is why option number C is correct, right? This is how you solve this particular question.