Question

The terminal velocity of a rain drop is $30cm/s$, If the viscosity of air is $1.8\times {10}^{-5}Ns{m}^{-2}$, The radius of rain drop is:

• A. $0.01mm$
• B. $0.5mm$
• C. $0.05mm$
• D. $1mm$

Answer 1

Answer: (C)

$0.05mm$

The terminal velocity $V$ of the body of radius $r$, density $\rho$ falling through a medium of density ${\rho }_o$ is given by
$V=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.
$\Rightarrow 30\times {10}^{-2}=\frac{2r^2(1000-1.2)\times 9.8}{9\times 1.8\times {10}^{-5}}\Rightarrow r^2=24.9\times {10}^{-10}\Rightarrow r=4.98\times {10}^{-5}m=4.98\times {10}^{-5}\times {10}^{3}mm=0.0498\approx 0.05mm$