Question

A raindrop with radius $1.5\, mm$ falls from a cloud at a height $1200\, m$ from ground. The density of water is $1000\, kgm ^{-3}$ and density of air is $1.2\, kgm ^{-3}$. Assume the drop was spherical throughout the fall and there is no air drag. The impact speed of the drop will be

• A. $27 \, km\,s^{-1} $
• B. $550 \, km\,s^{-1} $
• C. zero
• D. $129 \, km\,s^{-1} $

Answer 1

Answer: (B)

Acceleration of rain drop. $a=\left[\frac{\rho-\sigma}{\rho}\right] g$
where $\rho=$ density of water,
$\sigma=$ density of air.
$\therefore a=\left[\frac{1000-1.2}{1000}\right] \times 10=9.98 \,ms ^{-2}$
Here, $u=0$, and $s=1200 \,m$
Now, $v^{2}=u^{2}+2 a s $
$\therefore $ $v^{2}=(0)^{2}+2 \times 9.98 \times 1200$
$ \Rightarrow $ $v=154.7 \,ms ^{-1}=550 \,km \,s ^{-1}$