Q.

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

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a

nC

b

nC

c

n3C

d

n½C

answer is D.

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Detailed Solution

If p 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 nm=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

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