Calculate the viscous force acting on a rain drop of diameter 1 mm, falling with a uniform velocity 2 m/s through air. The coefficient of viscosity of air is 1.8 \(\times\) 10^{-5} Ns/m^{2}

Correct answer = 3.394 ×10^{-7 }N or 3.393 ×10^{-7 }N

Explaination::

Given: d= 1 mm, v_{0 }= 2 m/s, η= 1.8 × 10^{-5} Ns/m^{2}

r =d/2 =0.5 mm = 5 ×10^{-4 }m,

Solution:

By Stoke’s law the viscous force on rain drop is

f= 6πηr v_{0}

= 6 ×3.142 x 1.8 × 10^{-5 }x 5 ×10^{-4 }× 2

= 3.394 ×10^{-7 }N