Q. A marble of mass $x$ and diameter $2\ r$ is gently released a tall cylinder containing honey. If the marble displaces mass $y( < x)$ of the liquid, then the terminal velocity is proportional to
A) $(x + y)$
B) $(x - y)$
C) $\frac{x + y}{r}$
D) $\frac{(x - y)}{r}$
Explanation
(d) If $v$ is the terminal velocity, then
$xg - yg = 6\ \pi\ \eta\ r\ v$
Or $v = \frac{(x - y)}{r}\ \frac{g}{6\ \pi\ \eta}$
Or $v \propto \frac{(x - y)}{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.