Question

Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v$. The retarding viscous force acting on the spherical ball is:

• A. directly proportional to R but inversely proportional to v
• B. directly proportional to both radius R and velocity v
• C. inversely proportional to both radius R and velocity v
• D. inversely proportional to R but directly proportional to velocity v

Answer 1

The correct option is B directly proportional to both radius R and velocity v

Stoke's Law states,

Frictional force on a spherical object of radius R due to viscous medium of coefficient of viscosity $\eta =6\pi \eta Rv$

where $v$ is the instantaneous velocity of the object.

Thus $f\propto R$

$f\propto v$