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 R but directly proportional to velocity v
• D. inversely proportional to R but directly proportional to velocity v

Answer 1

Answer: (B)

Retarding force acting on a ball falling into a viscous fluid
$F=6 \pi \eta R v$ where
$R$ = radius of ball,
$v$ = velocity of ball and
$\eta=$ coefficient of viscosity
$\therefore F \propto R$ and $F \propto v$
Or in words, retarding force is directly proportional to both $R$ and $v$.