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)
JEE MAIN 2020, Medium
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After falling through h, the velocity be equal to terminal velocity
$\sqrt{2 gh }=\frac{2}{9} \frac{ r ^{2} g }{\eta}\left(\rho_{\ell}-\rho\right)$
$\Rightarrow h =\frac{2}{81} \frac{ r ^{4} g \left(\rho_{\ell}-\rho\right)^{2}}{\eta^{2}}$
$\Rightarrow h \propto r ^{4}$
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