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  4. A solid ball of volume V experiences a viscous force F when falling with a speed v in a liquid. If another ball of volume 8 V with the same velocity v is allowed to fall in the same liquid, it experiences a force

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Q. A solid ball of volume $V$ experiences a viscous force $F$ when falling with a speed $v$ in a liquid. If another ball of volume $8 \,V$ with the same velocity $v$ is allowed to fall in the same liquid, it experiences a force

Mechanical Properties of Fluids

Solution:

From stoke's law, $F =6 \pi \eta R _1 v$, and $V =\frac{4}{3} \pi R ^3$
$F^{\prime}=6 \pi \eta R_2 v,\left(\right.$ volume $\left.8 V=\frac{4}{3} \pi(2 R)^3\right)$
$=6 \pi \eta(2 R ) v =2 F$