Question

A ball of mass $m$ and radius $r$ is released in a viscous liquid. The density of the liquid is negligible compared to that of the ball.The value of its terminal velocity is proportional to:

• A. $\frac{1}{r}$ only
• B. $\frac{m}{r}$
• C. $\sqrt{\frac{m}{r}}$
• D. $m$ only

Answer 1

Answer: (B)

$\frac{m}{r}$

From the equation of terminal velocity we have $v=\frac{\left(\frac{2}{9}\right)r^{2}g(\rho -\sigma )}{\eta }$
here we see that
$v\propto r^2\rho$
or
$v\propto r^2\frac{m}{r^3}$
$v=K\frac{m}{r}$ where $K$ is constant.