Question

A ball of mass $m$ is thrown upwards with a velocity $v$. If air exerts an average resisting force $F$, the velocity with which the ball returns to the thrower is

• A. $v\sqrt{\frac{mg}{mg+F}}$
• B. $v\sqrt{\frac{F}{mg+F}}$
• C. $v\sqrt{\frac{mg-F}{mg+F}}$
• D. $v\sqrt{\frac{mg+F}{mg}}$

Answer 1

Answer: (C)

For upward motion,
Net force $=mg+F$
$\therefore$ Retardation $(a)=\frac{mg+F}{m}$
Distance, $s=\frac{v^2}{2a}=\frac{v^{2}m}{2(mg+F)}....(i)$
For downward motion, net force $=mg-F$
$\therefore$ Acceleration $\left(a^{\prime }\right)=\frac{mg-F}{m}$
Distance, $s^{\prime }=\frac{v^{\prime 2}}{2a^{\prime }}=\frac{v^{\prime 2}m}{2(mg-F)}...(ii)$
As $s=s^{\prime }\therefore \frac{v^{2}m}{2(mg+F)}=\frac{v^{\prime 2}m}{2(mg-F)}$
or $v^{\prime }=v\sqrt{\frac{mg-F}{mg+F}}$