Q 11-09-126JEE MainJEE Main 2020 (5 Sep, Shift 2)Easy
In an experiment to verify Stokes' law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is the same as its velocity just before entering the water surface, then the value of $h$ is proportional to: (ignore viscosity of air)
Answer: (A) $r^4$
Speed on reaching the water: $v = \sqrt{2gh}$.
Terminal speed in water: $v_t = \dfrac{2r^2(\rho-\sigma)g}{9\eta} \propto r^2$.
Equating, $\sqrt{2gh} \propto r^2$, so $h \propto r^4$.
Solution by Sreeraj P, M.Sc Physics