Q 11-09-040JEE MainJEE Main 2026 (24 Jan, Shift 1)Easy
Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10\ \text{cm/s}$ coalesce to form a bigger drop. The terminal velocity of bigger drop is
______ $\text{cm/s}$.
Numerical value type. Enter your answer.
Answer: 160
Volume is conserved: $\frac43\pi R^3 = 64\cdot\frac43\pi r^3\Rightarrow R = 4r$.
Terminal velocity $v\propto r^2$ (Stokes' law):
$$v' = 10\times4^2 = 160\ \text{cm/s}$$
Solution by Sreeraj P, M.Sc Physics