Question

The ratio of the terminal velocities of two drops of same density of radii $R$ and $R/2$ in air is

• A. $2$
• B. $1$
• C. $1/2$
• D. $4$

Answer 1

The correct option is D $4$

We know that,
Terminal velocity, $v=\frac{2}{9}{r}^{2}g\left(\frac{\rho -\sigma }{\eta }\right)$
Since both the drops are of same density and both are moving in same fluid,
$\Rightarrow v\propto r^2$
$\frac{v_1}{v_2}=\frac{r_1^2}{r_2^2}=\frac{(R{)}^2}{(R/2{)}^2}$
$\Rightarrow \frac{v_1}{v_2}=4$