Question

A metallic sphere of mass M falls through gllycerine 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. 2 v
• B. 4 v
• C. 8 v
• D. 16 v

Answer 1

Answer: (B)

4 v

Answer 2

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

$\therefore R^{3} = 8r^{3}$ or R = 2r

As $v \propto r^{2}$

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