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Question

Rain drops, each of radius r, are falling through air with steady velocity v. If eight drops coalesce to form a big drop, then the big drop so formed will fall with velocity ?

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Solution

Falling with uniform speed means the drops have acheived terminal speed. Let us find the radius R of the bigger drop in terms of the radius r of the smaller drop. We use conservation of volume to arrive at the result.
8×43πr3=43πR3R=2r
Now terminal speed is directly proportional to square of radius,
vv=r2R2=r2(2T)2
v=4v
Big drop will fall with velocity 4v.

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