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 ?

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.

Now terminal speed is directly proportional to square of radius,

$\therefore$ Big drop will fall with velocity $4v$.