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 Stoke's law, a drag force acts on a spherical body when it falls through a column of a viscous liquid with certain velocity. This resisting force acts in a direction opposite to the direction of motion of the body.

Mathematically, the magnitude of this force $F_d=6\pi \eta av$

where $\eta$ is the viscosity of the liquid

$a$ is the radius of the spherical body

$v$ is the velocity with which the body is falling