Q. Spherical ball of radius $R$ are falling in a viscous fluid of viscosity ɳ 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 $v$
Explanation
(b) Retarding force acting on a ball falling in to a viscous fluid
$F = 6\pi ɳRv$
$where\ \ \ R = radius\ of\ ball,$
$v = velocity\ of\ ball,$
$and\ ɳ = coefficient\ of\ viscosity$
$\therefore\ F \propto R\ and\ F \propto v$
Or in words, retarding force is directly proportional to both R and v.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.