Question

A ball dropped from a height of $2m$rebounds to a height of $1.5m$ after hitting the ground. Then, the percentage of energy lost is

• A. $25$
• B. $30$
• C. $50$
• D. $100$

Answer 1

The correct option is A

$25$

Step 1: Given data

Height from which ball is dropped, $H=2m$

Height to which ball rebound, $h=1.5m$

Step 2: Find the potential energy, P.E

Let mass of the ball is $m$

Potential energy at height $H$, ${\left(P.E\right)}_1=mgH$

Potential energy at height $h$, ${\left(P.E\right)}_2=mgh$

Step 3: Find the percentage loss in the potential energy

Loss in the potential energy, $∆P.E=mg(H-h)$

Percentage loss in the potential energy, $\%∆\left(P.E\right)=\left[\frac{mg(H-h)}{mgH}\times 100\right]\%$

$$\begin{gathered} =\left[\frac{mg(2-1.5)}{mg\times 2}\times 100\right]\% \\ =\left[\frac{0.5}{2}\times 100\right]\% \\ =25\% \end{gathered}$$

Hence, option (A) is correct.