Question

A small metal sphere of radius $a$ is falling with a velocity $v$ through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is $\eta$ then the sphere encounters an opposing force of

• A. $6\pi\eta a^{2}v$
• B. $\frac{6\eta v}{\pi a}$
• C. $6\pi\eta av$
• D. $\frac{\pi\eta v}{6a^{3}}$

Answer 1

Answer: (C)

$6\pi\eta av$

Answer 2

Stokes established that if a sphere of radius a moves with velocity $v$ through a fluid of viscosity $\eta$, the viscous force opposing the motion of the sphere is $F=6 \pi \eta a v$