Question

A rain drop of radius 0.3 mm has a terminal velocity of 1 m/s in air. The viscosity of air is $18\times {10}^{-5}$ poise. The viscous force on the drop is:

• A. $16.695\times {10}^{-7}$ N
• B. $1.695\times {10}^{-8}$ N
• C. $1.017\times {10}^{-12}$ N
• D. $101.73\times {10}^{-9}$ N

Answer 1

The correct option is D $101.73\times {10}^{-9}$ N

$r=0.3mm=0.3\times {10}^{-3}m$
$V_T=1m/s$
$\eta =18\times {10}^{-5}$ poise
$=18\times {10}^{-6}$ decapoise
Viscous force, $F=6\pi \eta r{V}_T$
$=6\times \frac{22}{7}\times 18\times {10}^{-6}\times 0.3\times {10}^{-3}\times 1$
$=101.73\times {10}^{-9}N$