Question

A tennis ball dropped from a height of $2m$ rebounds only $1.5m$ after hitting the ground. What fraction of its energy is lost in the impact?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{8}$

Answer 1

Answer: (A), (D)

$\frac{1}{8}$

Step 1: Given data

The initial height of the tennis ball, $h=2m$.

The rebound height, $h\text{'}=1.5m$

Step 2: Finding the energy lost

The expression for potential energy is written as $\mathrm{m}gh$, where $\mathrm{m}$ is the mass, $g$ is the acceleration due to gravity and $h$ is the height.

It is seen that potential energy is directly proportional to the height as the mass and acceleration due to gravity for a given body are constant.

The fraction of energy lost can be calculated by considering the height, as shown below:

$$\begin{gathered} \frac{h-h\text{'}}{h} \\ =\frac{2m-1.5m}{2m} \\ =\frac{0.5}{2} \\ =\frac{1}{4} \end{gathered}$$

The fraction of energy lost is $\frac{1}{4}$

Hence, option (d) is correct.