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Q.

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   x1 and in the other, x2 . 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

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a

14gdSx2−x12

b

gdSx2+x12

c

gdSx22+x12

d

34gdSx2−x12

answer is A.

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Detailed Solution

Δ U=Ui−Uf        =(dsx1)g(x12)+(dsx2)g(x22)−2×{ds(x1+x2)2g(x1+x2)4}        =12 dgs(x2−x1)×(x2−x1)2        =14 dgs(x2−x1)2
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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   x1 and in the other, x2 . 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