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
(1) gdS(x2 + x1)2
(2) (1/4)gdS(x2 - x1)2
(3) (3/4)gdS(x2 - x1)2
(4) gdS(x22 + x12)
