Question

A metallic sphere of mass M falls through glycerine with a terminal velocity v. If we drop a ball of mass 8M of same metal into a column of glycerine, the terminal velocity of the ball will be:

• A. 2v
• B. 4v
• C. 8v
• D. 16v

Answer 1

The correct option is B 4v

Terminal velocity $\left(V_T\right)=\frac{2}{9}\frac{[\rho -\sigma ]r^2}{\eta }$
$V_T\propto r^2$
mass of sphere $m=\frac{4}{3}\pi r^3\rho$
$m\propto r^3$
$\frac{r_1}{r_2}={\left(\frac{m_1}{m_2}\right)}^{\frac{1}{3}}={\left(\frac{m}{8m}\right)}^{\frac{1}{3}}$
$r_2=2r_1$
Use this result to calculate ratio of terminal velocity
$\frac{V_{T_1}}{V_{T_2}}=\frac{r_1^2}{r_2^2}=\frac{1}{4}$
$V_{T_2}=4v$