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)

$8\,cm\,s^{-1}$

Answer 2

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 $v_{2}=8\, cm\, s ^{-1}$