Question

Two hailstones with radii in the ratio of 1 : 2 fall from a great height through the atmosphere. Then the ratio of their momentum after they have attained terminal velocity is

• A. 1 : 1
• B. 1 : 4
• C. 1 : 16
• D. 1 : 32

Answer 1

The correct option is D 1 : 32

$p=mv$

where $p=$momentum

$m=$mass

$v=$velocity

$m\propto r^3$

Here $r=$radius

Now $v=\frac{2}{9}{r}^{2}g\frac{(d_2-d_1)}{n}$

where

$r=$radius of oil drop

$g=$acceleration due to gravity

$d_1=$density of body

$d_2=$density of medium

So $v\propto r^2$

As$p=mv$ and $m\propto r^3$, $v\propto r^2$

Therefore $p\propto r^5$

Hence $\frac{p_1}{p_2}=\frac{(r_1{)}^5}{(r_2{)}^5}$

Now $r_2=2r_1$

So $\frac{p_1}{p_2}=\frac{(r_1{)}^5}{(2r_1{)}^5}$

$\frac{p_1}{p_2}=\frac{1}{32}$

Hence the correct option is (D).