Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d$. The area of the base of both vessels is $S$ but the height of liquid in one vessel is $x_{1}$ and in the other, $x_{2}$. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

Question:

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d$. The area of the base of both vessels is $S$ but the height of liquid in one vessel is $x_{1}$ and in the other, $x_{2}$. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

1. $g d S\left(x_{2}^{2}+x_{1}^{2}\right)$

2. $g d S\left(x_{2}+x_{1}\right)^{2}$

3. $\frac{3}{4} g d S\left(x_{2}-x_{1}\right)^{2}$

4. $\frac{1}{4} g d S\left(x_{2}-x_{1}\right)^{2}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Mechanical Properties of Fluids chapter.

JEE Main Previous Year 4 Sep. 2020

Correct Option: 4

Solution: