Question

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volume is:

• A. $3:2$
• B. $4:9$
• C. $9:4$
• D. $27:8$

Answer 1

The correct option is D $27:8$

Terminal velocity of $1^{st}$= 9V
$9V=\frac{2g{r}^2(T-S)}{9\eta }$--------(1)
Terminal velocity of $2^{nd}$ = 4V
$4V=\frac{2g{r}_1^2(T-\sigma )}{9\eta }$----------(2)
$r=3V^{1/2}$
and $r_1=2V^{1/2}$
So, Ratio of their volumes =$r^3:r_1^3$
$=27V^{3/2}:8V^{3/2}$
$=27:8$