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Two raindrops of equal radius fall through air, each at the same steady (terminal) velocity v cm/s. If the two drops merge into one larger drop, what is its terminal velocity?
- 4 v
- (4)^(1/3) v
- 2 v
- 64 v
Correct answer: (4)^(1/3) v
Solution
For a sphere falling at terminal velocity in a viscous medium, v ~ r². When two equal drops coalesce, volume is conserved, giving R = (2)^(1/3) r. Then the new terminal velocity scales as (R/r)² = (2)^(2/3) = 4^(1/3), so v' = 4^(1/3) v.
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