Two raindrops reach the earth with different terminal velocities having the ratio 9 : 4 . The ratio of their volumes is

Question

TestHub · Accepted Answer

The terminal velocity of a spherical drop of radius $r$ is given by $v_{t} = \frac{2}{9} \frac{r ^{2} ( ρ - σ ) g}{η}$ .

Thus, $v_{t} \propto r^{2}$ .

Given $\frac{v _{t 1}}{v _{t 2}} = \frac{9}{4}$ .

$\frac{r _{1}^{2}}{r _{2}^{2}} = \frac{9}{4} \Rightarrow \frac{r _{1}}{r _{2}} = \frac{3}{2}$ .

The volume of a spherical drop is $V = \frac{4}{3} π r^{3}$ , which means $V \propto r^{3}$ .

The ratio of their volumes is $\frac{V _{1}}{V _{2}} = (\frac{r _{1}}{r _{2}})^{3} = (\frac{3}{2})^{3} = \frac{27}{8}$ .

Answer: $\frac{27}{8}$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion