An object falls from a height of 10 m above the ground. After striking the ground it loses $50 \%$ o

Question

An object falls from a height of 10 m above the ground. After striking the ground it loses $50 \%$ of its kinetic energy. The height upto which the object can rebounce from the ground is

Professor PC Thomas Classes · Answer

(d) : Given, height $(h)=10 \mathrm{~m}$ P.E. at $h=10 \mathrm{~m}$, P.E. $=m g 	imes 10=10 \mathrm{mg}$ Before striking ground, \ $ (	ext { K.E. })_i=P . E . 	ext { at } h=10 \mathrm{~m}=10 \mathrm{mg} $ \ After striking ground, $ \ \begin{aligned} & (	ext { K.E. })_f=50 \%(	ext { K.E. })_i=\frac{1}{2} 	imes 10 \mathrm{mg} \ & (	ext { K.E. })_f=5 \mathrm{mg} \end{aligned} $ \ when object rebounces to $h^{\prime}$, \ $ (K \cdot E .)_f=	ext { P.E. at } h^{\prime} $ So, $5 m g=m g h^{\prime} \Rightarrow h^{\prime}=5 \mathrm{~m}$