Question

Spherical balls of radius R are falling in a viscous fluid of viscosity n 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)

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 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 $ .