Question

Eight equal drops of water are falling through air with a steady velocity of $10\,cm\,s^{-1}$. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is

• A. $40 \,cm\, s^{-1}$
• B. $10 \,cm\, s^{-1}$
• C. $30\, cm\, s^{-1}$
• D. $80\, cm\, s^{-1}$

Answer 1

Answer: (A)

Here,
$v \propto r^{2}$
$\therefore \frac{v_{1}}{v_{2}} =\frac{r_{1}^{2}}{8^{2 / 3} \cdot r^{2}}$
$\frac{10}{v_{2}} =\frac{1}{4}$
$v_{2} =40\, cm / s$