Question

A drop of water of radius $0.0015 \,mm$ is falling in air. If the coefficient of viscosity of air is $2.0 \times 10^{-5} \,kg / ms$, the terminal velocity of the drop will be
(The density of water $=1.0 \times 10\, kg / m ^{3}$ and $g=10\, m / s ^{2}$ )

• A. $1.0 \times 10^{-4} \,m / s$
• B. $2.0 \times 10^{-4}\, m / s$
• C. $2.5 \times 10^{-4} \,m / s$
• D. $5.0 \times 10^{-4} \,m / s$

Answer 1

Answer: (C)

Radius $r=0.0015\, mm =15 \times 10^{-7} \,m$
Coefficient of viscosity $=2.0 \times 10^{-5} \,kg / ms$
Density of water $=1 \times 10^{3} \,kg\,m / m ^{3}$
Terminal velocity $v=\frac{2}{9} \frac{r^{2} \rho g}{\eta}$
$v=\frac{2}{9} \times \frac{\left(15 \times 10^{-7}\right)^{2} \times 1 \times 10^{3} \times 10}{2 \times 10^{-5}}$
$v=2.5 \times 10^{-4} \,m / s$
$\left(\right.$ The density of water $=1.0 \times 10^{3}\, kg / m ^{3}$ and $\left.g =10 \,m / s ^{2}\right)$