Question

The terminal velocity of a rain drop of radius $r$ is $ 2\,cm\,s^{-1}$ . If eight such identical drops combine to form a single large drop, the terminal velocity would be

• A. $ 1\,cm\,s^{-1}$
• B. $ 2\,cm\,s^{-1}$
• C. $ 4\,cm\,s^{-1}$
• D. $ 8\,cm\,s^{-1}$

Answer 1

Answer: (D)

If eight drops of same radius $r$ coalesce, then radius of new drop is given by $R$.
$\frac{4}{3} \pi R^{3}=8 \times \frac{4}{3} \pi r^{3}$
$R=2 r$
If drop of radius $r$ is falling in viscous medium, then it acquires a critical velocity $v$ and $v \propto r^{2}$
$\Rightarrow \frac{v_{2}}{v_{1}}=\left[\frac{R}{r}\right]^{2}$
$=\left[\frac{2 r}{r}\right]^{2}=4$
$v_{2}=4\, v_{1}$
or $v_{2}=8\, cm\, s ^{-1}$