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

Answer: (B)

directly proportional to both radius R and velocity v

Answer 2

Retarding force acting on a ball falling into a viscous fluid $F=6\pi \eta Rv$ where $R=$ radius of ball, $v\text{ }=$ 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 $v.$