Question

A marble of mass $x$ and diameter $2r$ is gently released in 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. $\frac{x-y}{r}$

Answer 1

The correct option is D $\frac{x-y}{r}$

We know that,
$v_0=\frac{2r^2(\rho -{\rho }^{,})g}{9\eta }$
Now,
$x=\frac{4}{3}\pi r^3\rho$ or $\rho \propto \frac{x}{r^3}$

Similarly, ${\rho }^{,}\propto \frac{y}{r^3}$
So, if we substitute both values into equation of $v_0$ we get,
$v_0\propto \frac{x-y}{r}$