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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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