Q. Speed of 2 cm radius ball in a viscous liquid is $20\ cms^{- 1}$. Then the speed of 1 cm radius ball in the same liquid is
A) $5\ cms^{- 1}$
B) $10\ cms^{- 1}$
C) $40\ cms^{- 1}$
D) $80\ cms^{- 1}$
Explanation
(a) Terminal velocity, $v = \frac{2r^{2}(\rho - \rho_{0})g}{9\ \eta}$
$ie,\ v \propto r^{2}$
$\therefore\frac{v_{1}}{v} = \frac{r_{1}^{2}}{r^{2}}$
Or $v_{1} = v\left( \frac{r_{1}}{r} \right)^{2}$
$= 20\ \left( \frac{1}{2} \right)^{2} = 5\ cms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.