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Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density \( \rho \). The height of the liquid in one vessel is \( h_{1} \) and that in the other \( h_{2} \). The area of either bases is \( A \). The work done by the gravity in equalizing the levels when the vessels are interconnected is
(a) \( \operatorname{A\rho g}\left[\frac{\left(h_{1}-h_{2}\right)}{2}\right] \)
(b) \( \operatorname{A\rho g}\left[\frac{\left(h_{1}+h_{2}\right)}{2}\right]^{2} \)
(c) \( \operatorname{A\rho g}\left[\frac{\left(h_{1}-h_{2}\right)}{4}\right] \)
(d) \( A \rho g\left[\frac{\left(h_{1}-h_{2}\right)}{2}\right]^{2} \)
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