Question

Two rain drops reach the earth with different terminal velocities having ratio $9:4$ . Then the ratio of their volumes is

• A. $3:2$
• B. $4:9$
• C. $9:4$
• D. $27:8$

Answer 1

Answer: (D)

We know that terminal velocity is
given by
$V_T=\frac{2}{9n}{r}^2\left({\rho }_s-{\rho }_1\right)$
$\therefore V_T\propto r^2$
$\therefore \frac{9}{4}={\left(\frac{r_1}{r_2}\right)}^2$
$\therefore \frac{r_1}{r_2}=\frac{3}{2}$
$\therefore \frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{3}{2}\right)}^3$
$\frac{V_1}{V_2}=27:8$