Question

A marble of mass $x$ and diameter $2r$ 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. $\left(\frac{x+y}{r}\right)$
• D. $\left(\frac{x-y}{r}\right)$

Answer 1

The correct option is D $\left(\frac{x-y}{r}\right)$

If $v$ is the terminal velocity , then
$xg-yg=6\pi \eta rv$
$v=\frac{(x-y)}{r}.\frac{g}{6\pi \eta }$
$v\alpha \frac{x-y}{r}$