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Q.

27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___ times that of a smaller drop.

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answer is 243.

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Detailed Solution

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$U = \frac{{KQ}^{2}}{2 R}$ ; $Q^{'} = nQ; R^{'} = n^{\frac{1}{3}} R$

$U^{'} = \frac{K {(Q^{'})}^{2}}{2 R^{'}} = n^{\frac{5}{3}} U$

$U^{'} = 3^{5} U = 243 U$

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27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___ times that of a smaller drop.