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64 spherical rain drops of equal size are falling vertically through air with a terminal velocity $1.5 \mathrm{~ms}^{-1}$. If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is
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$24 \mathrm{~ms}^{-1}$
Volume of big drop $=64 \times$ volume of a small drop
$\Rightarrow \frac{4}{3} \pi R^3=64 \times \frac{4}{3} \pi r^3 \Rightarrow R=4 r$
The terminal velocity of spherical rain drop
$\begin{aligned}
& v=\frac{2 r^2(\rho-\sigma)}{9 \eta} \Rightarrow v \propto r^2 \\
\Rightarrow \quad & \frac{v_1}{v_2}=\left(\frac{r}{R}\right)^2=\left(\frac{1}{4}\right)^2=\frac{1}{16} \\
\therefore \quad & v_2=16 v_1=16 \times 1.5=24 \mathrm{~ms}^{-1}
\end{aligned}$
$\Rightarrow \frac{4}{3} \pi R^3=64 \times \frac{4}{3} \pi r^3 \Rightarrow R=4 r$
The terminal velocity of spherical rain drop
$\begin{aligned}
& v=\frac{2 r^2(\rho-\sigma)}{9 \eta} \Rightarrow v \propto r^2 \\
\Rightarrow \quad & \frac{v_1}{v_2}=\left(\frac{r}{R}\right)^2=\left(\frac{1}{4}\right)^2=\frac{1}{16} \\
\therefore \quad & v_2=16 v_1=16 \times 1.5=24 \mathrm{~ms}^{-1}
\end{aligned}$
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