Question

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

• A. $5.02 \times 10^{-7} \,N$
• B. $1.018 \times 10^{-7} \,N$
• C. $1.05 \times 10^{-7} \,N$
• D. $2.058 \times 10^{-7}\, N$

Answer 1

Answer: (B)

Given, $r=0.3\, mm =0.3 \times 10^{-3}\, m , v=1 ms ^{-1}$
$\eta=18 \times 10^{-5}$ poise $=18 \times 10^{-6}$ decapoise
Viscous force, $F=6 \pi \eta r v$
$=6 \times \frac{22}{7} \times\left(18 \times 10^{-6}\right) \times\left(0.3 \times 10^{-3}\right) \times 1$
$=1.018 \times 10^{-7} \, N$