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:
Solution
<p>Since density is negligible hence Buoyancy force will be negligible</p>
<p>At terminal velocity.</p>
<p>$\mathrm{Mg} =6 \pi \eta \mathrm{rv}$</p>
<p>$\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad$ (as mass is constant)</p>
<p>Now, $\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$</p>
<p>$r^{\prime}=2 \mathrm{r}$</p>
<p>So, $v^{\prime}=\frac{v}{2}$</p>
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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