Q 11-09-019NEETJEE MainMedium
Two identical rain drops fall through air at terminal speed $v$. They merge into one bigger drop. The terminal speed of the bigger drop is
Answer: (B) $2^{2/3}v$
Concept. Terminal speed $\propto r^2$ (Stokes); merging conserves volume.
Step 1. New radius. Volume doubles: $R = 2^{1/3}r$.
Step 2. New speed. $v' = (2^{1/3})^2v = 2^{2/3}v$.
Answer. $2^{2/3}v$ (Option B).
Solution by Sreeraj P, M.Sc Physics