A ball of mass $10 \mathrm{~g}$ is allowed to fall down from 10 $\mathrm{m}$ height. After collision with the ground if $50 \%$ of its energy is lost, then the height reached by the ball is

• A

  $4 \mathrm{~m}$
• B

  $6 \mathrm{~m}$
• Correct answer
  C

  $5 \mathrm{~m}$
• D

  $7 \mathrm{~m}$

Solution

Mass of ball, $\mathrm{m}=10 \mathrm{~g}=10 \times 10^{-3} \mathrm{~kg}$ Height, $\mathrm{h}=10 \mathrm{~m}$ Apply the conservation of energy potential energy $=$ kinetic energy $\mathrm{K} . \mathrm{E}=\mathrm{mgh}=10 \mathrm{mg}...(i)$
$\mathrm{K} . \mathrm{E}^{\prime}=50 \% \mathrm{~K} . \mathrm{E}$ Use equation (1), we have $=5 \times 10 \mathrm{mg}$ $\begin{aligned} & =5 \mathrm{mg} \\ & \mathrm{P} \cdot \mathrm{E}^{\prime}=\mathrm{K} \cdot \mathrm{E}^{\prime}=\mathrm{mgh} \Rightarrow 5 \mathrm{mg}=\mathrm{mgh} \\ & \mathrm{h}=5 \mathrm{~m} . \end{aligned}$ The height reached by the ball is $5 \mathrm{~m}$.

Hence, the correct answer is option: 'C'.