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Two identical spherical raindrops, each of radius r, fall through air at terminal velocity v cm/s. When the two drops coalesce into one larger drop, what is the terminal velocity of the combined drop?

1. 4 v
2. (4)^(1/3) v
3. 2 v
4. 64 v

Correct answer: (4)^(1/3) v

Solution

Volume conservation: (4/3)*pi*R³ = 2*(4/3)*pi*r³ => R = 2^(1/3) r. Since v_T proportional to r²: v' = v * (2^(1/3))² = v * 4^(1/3).

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