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  4. A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

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Q. A small spherical ball falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

Mechanical Properties of Fluids

Solution:

If $\rho$ is the density of the ball and $\rho^{\prime}$ that of the another ball, $m$ for the balls are the same, but $r^{\prime}=2 r$
$\therefore m g=6 \pi r \eta v$ (by Stoke's law)
or, $ 6 \pi r \eta v=6 \pi 2 m v^{\prime}$ So, $v^{\prime}=\frac{v}{2}$