Question

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

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

Answer 1

Answer: (D)

$1:32$

As the density of hailstones are same,

Mass of first = $d\times \frac{4}{3}\pi r^3=M$

Velocity of first =$\frac{2r^2(T_h-T_a)g}{9\eta }=V$

For $2^{nd}$ hail with radius $=2r$,

Mass of $2^{nd}$= $d\times \frac{4}{3}\pi r^3{2}^3=8M$

Velocit of $2^{nd}$=$\frac{2g{r}^2(T_h-T_a)4}{9\eta }=4V$

Ratio of Momenta =$MV:8M\times 4V$

$MV:32MV=1:32$