A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

Dear student,

After the liquid in the two tubes reach equilibrium, the liquid initially at higher level decreases by height h/2, and liquid initially at lower level rises by height h/2.
Let the height of liquid in tube at lower level be.

Initailly the total gravitational potential energy of the sytem=

Finally the total gravitational potential energy of system =

Hence work done by gravitational force=Decrease in potential energy=