Question

A ball is allowed to fall from a height of $20\mathrm{m}$. If there is a $30\%$ loss of energy due to impact, then after one impact ball will go up to:

• A. $18\mathrm{m}$
• B. $16\mathrm{m}$
• C. $12\mathrm{m}$
• D. $14\mathrm{m}$

Answer 1

The correct option is D

$14\mathrm{m}$

Step 1: Given data

Let mass of the ball $=\mathrm{m}$

Let before impact, the potential energy of a ball is, ${\mathrm{E}}_1={\mathrm{mgh}}_1$

Here, height of the ball before impact ${\mathrm{h}}_1=20\mathrm{m}$

Let after impact, the potential energy of a ball is, ${\mathrm{E}}_2={\mathrm{mgh}}_2$

Here, height of the ball after impact$={\mathrm{h}}_2$

Step 2: Calculating height of a ball after a loss of $30\%$ energy due to impact

Now according to the question, $30\%$ of the energy is lost in an impact which means only $70\%$ is left after impact. Hence,

$$\begin{gathered} {\mathrm{E}}_2=0.7{\mathrm{E}}_1 \\ \Rightarrow {\mathrm{mgh}}_2=0.7{\mathrm{mgh}}_1 \\ \Rightarrow {\mathrm{h}}_2=0.7{\mathrm{h}}_1 \\ \Rightarrow {\mathrm{h}}_2=0.7\times 20 \\ \Rightarrow {\mathrm{h}}_2=14\mathrm{m} \end{gathered}$$

Therefore the height of a ball after a loss of $30\%$ energy is equal to $14\mathrm{m}$

Hence, option(D) is correct answer.