Question

A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.

• A. mg
• B. 2mg
• C. 2.5mg

Answer 1

The correct option is A mg

A ball of mass m is dropped onto a floor from a certain height let 'h'.
$\therefore v_1=\sqrt{2gh},v_1=0,v_2=-\sqrt{2gh}\&v_2=0$
$\therefore$ Rate of change of velocity:-
$F=\frac{m\times 2\sqrt{2gh}}{t}$
$\therefore v=\sqrt{2gh},s=h,v=0$
$\Rightarrow v=u+at$
$\Rightarrow \sqrt{2gh}=gt\Rightarrow t=\sqrt{\frac{2h}{g}}$
$\therefore Totaltime2\sqrt{\frac{2h}{t}}$
$\therefore F=\frac{m\times 2\sqrt{2gh}}{2\sqrt{\frac{2h}{g}}}=mg$