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) $16$
Volume is conserved: $64r^3 = R^3$, so $r = \dfrac{R}{4}$.
Terminal velocity $v = \dfrac{2r^2(\rho - \sigma)g}{9\eta} \propto r^2$, so
$$\frac{v_1}{v_2} = \left(\frac{R}{r}\right)^2 = 16$$
Solution by Sreeraj P, M.Sc Physics