A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water $f_{\mathrm{w}}=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ and Density of
air $f_{\mathrm{a}}=1.2 \mathrm{~kg} \mathrm{~m}{ }^{-3}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$
Coefficient of viscosity of air $=1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$ ]
Correct Option: , 3
At terminal speed
$\mathrm{a}=0$
$\mathrm{F}_{\text {net }}=0$
$m g=F_{v}=6 \pi \eta R v$
$\mathrm{v}=\frac{\mathrm{mg}}{6 \pi \eta \mathrm{Rv}}$
$\mathrm{v}=\frac{\rho_{\mathrm{w}} \frac{4 \pi}{3} \mathrm{R}^{3} \mathrm{~g}}{6 \pi \eta \mathrm{R}}$
$=\frac{2 \rho_{w} R^{2} g}{9 \eta}$
$=\frac{400}{81} \mathrm{~m} / \mathrm{s}$
$=4.94 \mathrm{~m} / \mathrm{s}$