Q 11-09-029JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into $64$ identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1/v_2$ is ______.
Answer: (D) $16$
Concept. Terminal velocity $v_t=\dfrac{2r^2(\rho-\sigma)g}{9\eta}\propto r^2$. 64 droplets of the same total volume have radius $R/4$.
Step 1. Ratio. $\dfrac{v_1}{v_2}=\left(\dfrac{R}{R/4}\right)^2=16$.
Answer. Option D.
Solution by Sreeraj P, M.Sc Physics
