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JEE Main 2020 (5 Sep, Shift 2) · Terminal Velocity

Terminal Velocity question from JEE Main 2020 (5 Sep, Shift 2)

Q47JEE Main 2020 · 5 SEP · SHIFT 2Medium

Terminal Velocity

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 same as its velocity just before entering the water surface, then the value of h is proportional to:

(ignore viscosity of air)

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Answer: (b)

Speed after falling $h$ in air: $v = \sqrt{2gh}$ .
Terminal velocity in water: $v_t = \dfrac{2r^2(\rho - \rho_w)g}{9\eta} \propto r^2$ .
$\sqrt{2gh} = v_t \Rightarrow h = \dfrac{v_t^2}{2g} \propto (r^2)^2 = r^4$
So the answer is (b) $r^4$ .

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