Two identical cylindrical vessels with their bases at same level each contains a liquid of density ρ ρ . The height of the liquid in one vessel is h 1 and that in the other vessel is h 2 . The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected, is
Text Solution
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If h is the common height when they are connected, by conservation of mass
[as 
given]
As (h 1 /2) and (h 2 /2) are heights of initial centre of gravity of liquid in two vessels., the initial potential
energy of the system
...(i)
When vessels are connected the height of center of gravity of liquid in each vessel will be h/2,
i.e. ( 
[as 
Final potential energy of the system
…(ii)
Work done by gravity
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