Question

A ball of mass m is released from height h.. if coefficient of restitution e=1/2. the energy loss during the collision of the ball with the ground

• A. $\frac{1}{2}mgh$
• B. $\frac{1}{4}mgh$
• C. $\frac{3}{4}mgh$
• D. zero

Answer 1

The correct option is A $\frac{1}{2}mgh$

Velocity just before collision is $u=\sqrt{2gh}$ and energy is $E=mgh$

and the velocity just after the collision will be $v=eu=\frac{1}{2}\sqrt{2gh}$

so new energy will be $E_0=\frac{1}{2}m{v}^2=\frac{mgh}{2}$

so loss in enrgy will be $E-E_0=\frac{mgh}{2}$