Question

Spherical balls of radius R are falling in a viscous fluid of 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.

Retarding force acting on a ball falling into a viscous fluid $F=6\pi \eta Rv$

Where $R=$Radius of ball

$v=$velocity of ball

$\eta =$coefficient of viscosity

$\therefore F\propto R$ and $F\propto v$ or in words,

Retarding force is directly proportional to both $R$ and $v$