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Two cyllindrical vessels of equal cross ...

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`

Text Solution

Verified by Experts

The correct Answer is:
`(gArho)/(4)(h_(t) - h_(2))^(2)`
Let `h` be level in equilibrium. Equating the volumes, we have
`Ah_(1) + Ah_(2) = 2Ah`
`:. H = ((h_(1) + h_(2))/(2))`
Work done by gravity `= U_(i) - U_(f)`
Work `W = (m_(1)gh_(1)/(2) + m_(2)gh_(2)/(2)) - (m_(1) + m_(2))g h/(2)`
`= (Ah_(1)rhogh_(1))/(2) + (Ah_(2)rhogh_(2))/(2) - [Ah_(1) - Ah_(2)rho + Ah_(2)rholg((h_(1) + h_(2))/(4))`
Simplifying this, we get
`W = (rhoAg)/(4)(h_(1) - h_(2))^(2)`
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