Question

A steel ball of mass $m$ falls in a viscous liquid with terminal velocity $v$, then the steel ball of mass $8m$ will fall in the same liquid with terminal velocity:

• A. $v$
• B. $4v$
• C. $8v$
• D. $16\sqrt{2}v$

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 $V\propto r^2$
$\Rightarrow V\propto (volume{)}^{2/3}$
$\Rightarrow V\propto (m{)}^{2/3}$
$\Rightarrow \frac{V_2}{V_1}={\left(\frac{m_2}{m_1}\right)}^{2/3}$
$\Rightarrow \frac{V_2}{V}={\left(\frac{8m}{m}\right)}^{2/3}$
$\Rightarrow V_2=4V$