Question

Two small spherical drops having radii in the ratio $4:3$ fall from a height through the atmosphere. Their momenta on reaching the earth are in the ratio

• A. $4:4$
• B. $1:2$
• C. $4:2$
• D. $5:1$

Answer 1

Answer: (C)

$P=mv$
Terminal Velocity $v\propto r^2$
$\Rightarrow \frac{v_1}{v_2}={\left(\frac{r_1}{r_2}\right)}^2=\frac{16}{9}$
mass $=\frac{4}{3}\pi r^3\rho$
$\Rightarrow m\propto r^3$
$\therefore$ Momentums are in ratio
$\frac{P_1}{P_2}=\frac{r_1^3}{r_2^3}\times \frac{v_1}{v_2}$
$={\left(\frac{4}{3}\right)}^3\times \frac{16}{9}$
$=\frac{64}{27}=\frac{1024}{243}=4:2$