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

The correct option is D $27:8$

Terminal velocity, $v_T\alpha r^2$
$\frac{v_{T_1}}{v_{T_2}}=\frac{r_1^2}{r_2^2}=\frac{9}{4}$
$\frac{r_1}{r_2}=\sqrt{\frac{9}{4}}=\frac{3}{2}$
Volume of the drop is
$\therefore V=\frac{4}{3}\pi r^3$
$\frac{V_1}{V_2}=\frac{r_1^3}{r_2^3}=\frac{27}{8}$
Hence, the correct answer is option (d).