Question

The mass of a lead ball is M. It falls down in a viscous liquid with terminal velocity V. The terminal velocity of another lead ball of mass 8M in the same liquid will be:

• A. $64V$
• B. $4V$
• C. $8V$
• D. $V$

Answer 1

Answer: (B)

$4V$

The terminal velocity $V$ of the body of radius $r$, density
$\rho$ falling through a medium of density ${\rho }_o$ is given by
$V=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.
clearly $V\propto r^2$
$\Rightarrow V\propto (volume{)}^{2/3}$
$\Rightarrow V\propto (M{)}^{2/3}$
$\Rightarrow \frac{V_2}{V_1}={\left(\frac{M_2}{M_1}\right)}^{2/3}$
$\Rightarrow \frac{V_2}{V}={\left(\frac{8M}{M}\right)}^{2/3}$
$\Rightarrow V_2=4V$