Q. A metallic sphere of mass $M$ falls through glycerine with a terminal velocity $v$. If we drop a ball of mass $8\ M$ of same metal into a column of glycerine, the terminal velocity of the ball will be
A) $2\ v$
B) $4\ v$
C) $8\ v$
D) $16\ v$
Explanation
(b) $M = \frac{4}{3}\pi r^{3}\rho$ and $8M = \frac{4}{3}\pi\ R^{3}\rho$
So $R^{3} = 8\ r^{3}$
So $R = 2r$; Now $v \propto r^{2}$ so,
$\frac{v_{1}}{v} = \left( \frac{2r}{r} \right)^{2} = 4$ or $v_{1} = 4v$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.