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Question

# If n drops, each of capacitance C, coalesce to form a single big drop, the capacitance of the big drop will be

A

Vn2/3

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B

Vn1/3

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C

Vn1/3

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D

Vn2/3

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Solution

## The correct option is D Vn2/3 If ρ is the density of a small drop and r its radius, then the mass of each small drop is m=4π3r3ρ. If n such drops coalesce to form a big drop of radius R, then the mass of the big drop is n m=4π3R3ρ. Now, by conservation of mass: n*4π3r3ρ. = 4π3R3ρ. Hence, R=n13r. Now, the capacitance of a sphere is proportional to its radius. Hence the capacitance of the big drop will be C′=n13C. Hence, the correct choice is (d).

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