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

• A

  $\frac{1}{4}gdS{\left(x_2-x_1\right)}^2$

• B

  $gdS{\left(x_2+x_1\right)}^2$

• C

  $gdS\left(x_2^2+x_1^2\right)$

• D

  $\frac{3}{4}gdS{\left(x_2-x_1\right)}^2$