A small spherical ball of radius r , falling through a viscous medium of negligible density has term

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9-1.Fluid Mechanics

hard

A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity ' $v$ '. Another ball of the same mass but of radius $2 r$, falling through the same viscous medium will have terminal velocity:

A

$\frac{\mathrm{v}}{2}$

B

$\frac{\mathrm{v}}{4}$

C

$4 \mathrm{v}$

D

$2 \mathrm{v}$

(JEE MAIN-2024)

Solution

Since density is negligible hence Buoyancy force will be negligibleAt terminal velocity.

${Mg}=6 \pi \eta \mathrm{rv}$

$\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad$ (as mass is constant)

Now, $\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$

$r^{\prime}=2 \mathrm{r}$

So, $v^{\prime}=\frac{v}{2}$

Standard 11

Physics

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