Question

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

• A. $Onefourththeinitialheight$
• B. $Halftheinitialheight$
• C. $Threefourthinitialheight$
• D. $Noneofthese$

Answer 1

The correct option is B $Halftheinitialheight$

Let h be the height from which the ball has been dropped

So, loss in kinetic energy $\Delta K=50$

Let H is the height from where the ball is placed.

$U=mgH$

As the ball is released the potential energy is converted into kinetic energy.

When the ball strikes the earth, net potential energy is converted into kinetic energy as

$K=mgH$

So, loss in kinetic energy is

$\Delta K=\frac{50}{100}mgH$

$\Delta K=\frac{mgH}{2}$

$also,$

$\Delta K=K_f-K_i$

$K_f=\Delta K-K_i$

$K_f=\frac{mgH}{2}-mgH$

$K_f=\frac{mgH}{2}$

This kinetic energy will take the ball to the height where the potential energy of the ball will be

$U^{\prime }=\frac{mgH}{2}$

Hence, the ball will rise to half the height from where it was dropped.

Hence, the height attained $=\frac{1}{2}\left(initialheight\right)$