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Viscous Force

Uniform speed...

Question

Uniform speed of $2$ cm diameter ball is $20$ cm/s in a viscous liquid Then the speed of 1 cm diameter ball in the same liquid is?

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Solution

$v_{t} \propto r^{2} ⟹ \frac{v_{2}}{v_{1}} = {(\frac{r_{2}}{r_{1}})}^{2}$
$= {(\frac{1}{2})}^{2} = \frac{1}{4}$
$⟹ v_{2} = \frac{v_{1}}{4} = 5 \frac{c m}{s}$

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