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  4. A solid sphere of volume V experiences a viscous force F when descending with a speed v in a liquid. If another solid sphere of volume 27 V descends with the same speed v in the same liquid, it experiences a viscous force

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Q. A solid sphere of volume $V$ experiences a viscous force $F$ when descending with a speed $v$ in a liquid. If another solid sphere of volume $27 \,V$ descends with the same speed $v$ in the same liquid, it experiences a viscous force

KEAMKEAM 2020

Solution:

Viscous force $F=6 \pi \eta r v$
$\Rightarrow F a r$
But $r \times V^{1 / 3} $
(hence $V=\frac{4}{3} \pi r^{3}$ )
$\Rightarrow \frac{F'}{F}=\left(\frac{V'}{V}\right)^{1 / 3}$
$=\left(\frac{27 V}{V}\right)^{1 / 3}=3$
$\therefore F'=3 F$