Question

Two identical cylindrical vessels with their bases at the same level contain a liquid of density ρ.The height of liquid in one vessel is h₁ and that in the other vessel is h₂. The areas of either base is A. What is the work done by gravity in equalizing the levels when the two vessels are connected.

Answer 1

The centre of gravity of liquid columns would be at heights h₁ and h₂ respectively. A is area of crosssection. 

Total P.E. when they are not connected

When the levels are equal, the potential energy is given as

The change in potential energy 

Work done due to gravity

The negative sign shows that the work is done by the gravitational field on the liquid.