Question

A ball of mass $m$ and radius $r$ is released in a viscous liquid. The value of its terminal velocity is proportional to

• A. $mr$
• B. $\frac{m}{r}$
• C. ${\left(\frac{m}{r}\right)}^{1/2}$
• D. $m$

Answer 1

The correct option is B $\frac{m}{r}$

Lets consider $m=$ mass of a ball
$r=$ radius of a ball
$v_T=$ Terminal velocity
${\rho }_B=$ density of ball
${\rho }_L=$ density of liquid
$\mu =$ viscosity of liquid
We know that, $v_T=\frac{2({\rho }_B-{\rho }_L)r^{2}g}{9\mu }$
$\therefore v_T\propto r^2{\rho }_B$
$\Rightarrow v_T\propto r^2\frac{m}{r^3}$
$\Rightarrow v_T\propto \frac{m}{r}$