Question

A metallic sphere of mass M falls through glycerine with a terminal velocity v. If we drop a ball of mass 8 M 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

Answer: (B)

4v

mass of sphere $M=\frac{4}{3}\pi r^3\rho$

and $8M=\frac{4}{3}\pi R^3\rho$

$\because R^3=8r^3$ or $R=2r$

As $v\propto r^2$

$\therefore \frac{v^{\prime }}{v}={\left(\frac{R}{r}\right)}^2={\left(\frac{2r}{r}\right)}^2=4$ or $v^{\prime }=4v$