Question

A drop of water of radius $0.0015mm$ 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 $=1.0\times 10kg/m^3$ and $g=10m/s^2$ )

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