A ball of mass m and radius r is gently released in a viscous liquid.mass of liquid displaced by it

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9-1.Fluid Mechanics

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A ball of mass $m$ and radius $r$ is gently released in a viscous liquid.The mass of the liquid displaced by it is $m'$ such that $m\, >\, m'$ . The terminal velocity is proportional to

A

$\frac{{m\, - \,m'}}{r}$

B

$\frac{{m\, + \,m'}}{r}$

C

$\frac{{m\, + \,m'}}{r^2}$

D

$(m\, - \,m'){r^2}$

Solution

$\mathrm{mg}=\mathrm{m}^{\prime} \mathrm{g}+6 \pi \eta \mathrm{rV}$

$\Rightarrow v \propto \frac{m-m^{\prime}}{r}$

Standard 11

Physics

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