64 small drops of water having the same charge and same radius are combined to form one big drop. The ratio of capacitance of big drop to small drop is

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1 : 4

2 : 1

1 : 2

4 : 1

answer is A.

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Detailed Solution

Let r and R be the radii of small and big drops respectively. Then
$\frac{4}{3} {πR}^{3} = 64 \times \frac{4}{3} {πr}^{3} = (4)^{3} \times \frac{4}{3} {πr}^{3} ∴ R = 4 r$
Further $C \propto r$
$∴ \frac{(C)_{big}}{(C)_{small}} = \frac{4 r}{r} = \frac{4}{1}$

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