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When a number of liquid drops each of surface charge density s and energy E combine, a large drop is formed. If the charge density of the large drop is 3s, its energy is

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81E

27E

243 E

answer is D.

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Detailed Solution

$\begin{array}{l} σ_{big} = n^{1 / 3} σ_{small} \\ 3 S = n^{1 / 3} S \Rightarrow n^{1 / 3} = 3 \Rightarrow n = 27 \\ U_{big} = n^{5 / 3} U_{small} = (27)^{5 / 3} U_{s} = {(3^{3})}^{5 / 3} = 3^{5} U_{s} \\ U_{big} = 243 E \end{array}$

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