Q. A ball of mass $m$ and radius $r$ is released in a viscous liquid. The value of its terminal velocity is proportional
A) $\frac{1}{r}$
B) $\frac{m}{r}$
C) $\sqrt{\frac{m}{r}}$
D) $m$ only
Explanation
(b) $v = \frac{2r^{2}\rho g}{9\eta}\ r \Rightarrow v \propto r^{2}\rho$
But mass, $m = \frac{4}{3}\pi r^{3}\rho$ or $\rho \propto m/r^{3};$
Hence, $v \propto r^{2}(m/r^{3})$ or $v \propto m/r$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.