Question

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

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

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.
$\therefore a=\left[\frac{1000-1.2}{1000}\right]\times 10=9.98m{s}^{-2}$
Here, $u=0$, and $s=1200m$
Now, $v^2=u^2+2as$
$\therefore$ $v^2=(0{)}^2+2\times 9.98\times 1200$
$\Rightarrow$ $v=154.7m{s}^{-1}=550km{s}^{-1}$