Question

Two rain drops reach the earth with their terminal velocities in the ratio 4:9. The ratio of their radii is:

• A. 4: 9
• B. 2 : 3
• C. 3 : 2
• D. 9: 4

Answer 1

Answer: (B)

2 : 3

Ratio of Terminal velocities = 4:9
Let their radii r and $r_1$ respectively,
$\frac{\frac{2g{r}^2(T-\sigma )}{9\eta }}{\frac{2g{r}_1^2(T-\sigma )}{9\eta }}=\frac{4}{9}\Rightarrow \frac{r^2}{r_1^2}=\frac{4}{9}$

$\Rightarrow \frac{r}{r_1}=\frac{2}{3}\Rightarrow r:r_1=2:3$