Two identical cylindrical vessels each of area of cross-section A are on a level ground. Each contains a liquid of density $' ρ'$ . The heights of liquid columns are $h_{1} and h_{2}$ . If the two vessels are connected by means of a narrow pipe at the bottom, the work done by gravity in equalizing the liquid levels is,

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\frac{A ρ g}{4} {(h_{1} - h_{2})}^{2}

\frac{A ρ g}{2} (h_{1}^{2} - h_{2}^{2})

\frac{A ρ g}{4} (h_{1}^{2} - h_{2}^{2})

\frac{A ρ g {(h_{1} - h_{2})}^{2}}{2}

answer is D.

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Detailed Solution

Water final level height $(h) = \frac{h_{1} - h_{2}}{2}$

Mass of water disended $= A (\frac{h_{1} - h_{2}}{2}) ρ$

$= A (\frac{h_{1} - h_{2}}{2}) ρ . g (\frac{h_{1} - h_{2}}{2})$

$= \frac{A}{4} l g {(h_{1} - h_{2})}^{2}$

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