' $n$ ' small drops of same size fall through air with constant velocity $5 \mathrm{~cm} / \mathrm{s}$. They coalesce to form a big drop. The terminal velocity of the big drop is

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Volume }=\frac{4}{3} \pi r^3 n=\frac{4}{3} \pi R^3 \ & 	herefore \mathrm{R}=\mathrm{n}^{1 / 3} \mathrm{r} 	herefore \frac{\mathrm{R}}{\mathrm{r}}=\mathrm{n}^{\frac{1}{3}} \end{aligned}$ Terminal velocity, $\mathrm{v} \propto \mathrm{r}^2$ $\begin{aligned} & \frac{\mathrm{v}_2}{\mathrm{v}_1}=\left(\frac{\mathrm{r}_2}{\mathrm{r}_1}ight)^2=\left(\frac{\mathrm{R}}{\mathrm{r}}ight)^2=\mathrm{n}^{2 / 3} \ & 	herefore \mathrm{v}_2=\mathrm{n}^{2 / 3} \mathrm{v}_1=5 \mathrm{n}^{2 / 3} \mathrm{~m} / \mathrm{s} \end{aligned}$

' $n$ ' small drops of same size fall through air with constant velocity $5 \mathrm{~cm} / \mathrm{s}$. They…

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