Two cyllindrical vessels of equal cross sectional ara A contain water upto heights `h_1` and `h_2`. The vessels are interconnected so that the levels in them become equal. Calculate the work done by the force of gravity during the process. The density of water is `rho`

Explanation

Since the mass of water remains same
`rhoAh_1+rhoAh_2=rhoAh+rhoAhimpliesh=(h_1+h_2)/(2)`
`U_1=(rhoAh_1)g(h_1)/(2)+(rhoAh_2)g(h_2)/(2)=(rhoAg)/(2)(h_1^2+h_2^2)`
`U_2=(rhoAh)g(h)/(2)xx2=(rhoAg(h_1+h_2)^2)/(4)`
Since the gravitational force is conservative force, then
`W_(gr)=U_1-U_2=(rhoAg)/(4)(h_1+h_2)^2`