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  4. A sphere of mass M and radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

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Q. A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

AIIMSAIIMS 2004Mechanical Properties of Fluids

Solution:

$
V _{0}=\frac{2}{9} \frac{ R ^{3}\left(\rho-\rho^{\prime}\right) g }{ R \eta }
$
But $m =\frac{4}{3} \pi R ^{3} \rho$ or $m \propto R ^{3}$
$
V_{0} \propto \frac{M}{R}
$