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 h2 and h3 . If the two vessels are connected by means of a narrow pipe at the bottom, the workdone by gravity is equalizing the liquid levels is

W=Aρg4(h1−h2)2=Aρg4(h2−h3)2=Aρgh2144

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 h2 and h3 . If the two vessels are connected by means of a narrow pipe at the bottom, the workdone by gravity is equalizing the liquid levels is

W=Aρg4(h1−h2)2=Aρg4(h2−h3)2=Aρgh2144

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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 $\frac{h}{2}$ and $\frac{h}{3}$ . If the two vessels are connected by means of a narrow pipe at the bottom, the workdone by gravity is equalizing the liquid levels is

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$\frac{5 A ρ g h^{2}}{144}$

$\frac{5 A ρ g h^{2}}{72}$

$\frac{A ρ g h^{2}}{72}$

$\frac{A ρ g h^{2}}{144}$

answer is C.

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Detailed Solution

$W = \frac{A ρ g}{4} {(h_{1} - h_{2})}^{2} = \frac{A ρ g}{4} {(\frac{h}{2} - \frac{h}{3})}^{2} = \frac{A ρ g h^{2}}{144}$

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