Question

A ball of mass $600\text{g}$ is dropped to the ground from a height of $25\text{m}$. If the energy of the ball reduces by $35\%$ after striking the ground, what is the height to which it rebounds?

• A. $20\text{m}$
• B. $16.25\text{m}$
• C. $17.16\text{m}$
• D. $18.02\text{m}$

Answer 1

The correct option is B $16.25\text{m}$

According to law of conservation of energy:
The energy of the ball as it is striking the ground is equal to the potential energy of the ball when it is at a height of $25\text{m}$.
i.e $E_{\text{ball}}=mgh$
$\Rightarrow E_{\text{ball}}=0.6\times 10\times 25=150\text{J}$
$35\%$ of this energy is lost when the ball strikes the ground.
Remaining energy available to the ball to rebound $=\frac{65}{100}\times 150=97.5\text{J}$
This energy is available for the ball to rebound.

Suppose the ball rebounds to a height $h^{\prime }$. Then this entire energy will be converted to the potential energy at height $h^{\prime }$.
Therefore,
$mg{h}^{\prime }=0.6\times 10\times h^{\prime }=97.5$
$\Rightarrow h^{\prime }=16.25\text{m}$