Question

Raindrops are falling from a certain height. Assume all raindrops are spherical and have same drag coefficient. The impact speed of large raindrops compared to that of small raindrops is

• A. greater
• B. smaller
• C. same
• D. depends on height

Answer 1

Answer: (A)

greater

Answer 2

When the raindrops attains terminal velocity the net force acting on the body is zero.
$\therefore W-T-F=0$ or $F=W-T$
$\Rightarrow 6 \pi \eta r v=\frac{4}{3} \pi r^{3} \rho g-\frac{4}{3} \pi r^{3} \sigma g$
$=\frac{4}{3} \pi r^{3}(\rho-\sigma) g$
$\therefore$ Terminal velocity $v=\frac{2}{9} \frac{r^{2}(\rho-\sigma) g}{\eta}$ or $v \propto r^{2}$
Hence, the impact speed of large raindrops is greater as compared to the small raindrops.