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 $\propto r^{2}$
$\therefore \frac{V}{V_{1}}=\frac{r^{2}}{2^{2 / 3} \cdot r^{2}}$
$\Rightarrow V_{1}=\sqrt[3]{4} \cdot v$