Question

The terminal velocity of a liquid drop of radius ' $r$ ' falling through air is $v$. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air)

• A. $\sqrt{2}v$
• B. 2 v
• C. $\sqrt[3]{4}v$
• D. $\sqrt[3]{2}v$

Answer 1

Answer: (C)

Terminal velocity
$V=\frac{2}{9}\frac{r^2(\rho -\sigma )g}{\eta }$
When, the two drops of same radius $r$ coalesce then radius of new drop is $R$.
$\therefore \frac{4}{3}\pi R^3=\frac{4}{3}\pi r^3+\frac{4}{3}\pi r^3$
$\Rightarrow R=2^{1/3}\cdot r$
Critical velocity $\propto r^2$
$\therefore \frac{V}{V_1}=\frac{r^2}{2^{2/3}\cdot r^2}$
$\Rightarrow V_1=\sqrt[3]{4}\cdot v$