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
$\frac{P_{1}}{P_{2}}=\frac{r_{1}^{3}}{r_{2}^{3}} \times \frac{v_{1}}{v_{2}}$
$=\left(\frac{4}{3}\right)^{3} \times \frac{16}{9}$
$=\frac{64}{27}=\frac{1024}{243}=4: 2$