Question

A ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

• A. One fourth the initial height
• B. Half the initial height
• C. Three fourth initial height
• D. None of these

Answer 1

The correct option is B

Half the initial height

Step 1: Definition of kinetic energy and potential energy

Kinetic energy

1. The energy possessed by a body due to its motion is known as kinetic energy(K.E) of that body.
2. Kinetic energy is calculated using a formula:

$K.E=\frac{1}{2}m{v}^2$

Potential energy

1. The energy stored in a body due to its position or configuration is understood as its potential energy(P.E)
2. Potential energy is calculated using a formula:

$P.E=mgh$

Step 2: Calculating the height of a ball after striking the ground

We know, that the law of conservation of energy says:

$$\begin{gathered} P.E=K.E \\ mgh=K.E \\ h=\frac{K.E}{mg} \end{gathered}$$

After striking the ground, $50\%$ of the kinetic energy is lost. Hence, we have now only $50\%$of kinetic energy remaining.

Therefore, new kinetic energy is,

$$\begin{gathered} {(K.E)}^{\text{'}}=50\%ofK.E \\ \left(mg{h}^{\text{'}}\right)=0.5\times K.E \\ {h}^{\text{'}}=\frac{1}{2}\times \frac{K.E}{mg} \\ {h}^{\text{'}}=\frac{1}{2}\times h(\because \frac{K.E}{mg}=h) \\ {h}^{\text{'}}=\frac{h}{2} \end{gathered}$$

Hence, the Ball will attain a height equal to the half of the original height, after striking the ground.

Hence, option(B) is correct answer.