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

The correct option is C $6\pi \eta av$

According to the Stokes's Law,

The force of viscosity on a small sphere moving through a viscous fluid is given by:

$F=6\pi \eta av$

where: $F$ is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle

$\eta$ is the dynamic viscosity

$a$ is the radius of the spherical object

$v$ is the flow velocity relative to the object.