Question

If the coefficient of restitution be $0.5$, what is the percentage loss of energy on each rebounding of a ball dropped from a height?
(A) $12.5\%$
(B) $25\%$
(C) $50\%$
(D) $75\%$

Answer 1

The percentage loss of energy on each rebounding of a ball dropped from the height is determined by using the percentage loss in kinetic energy formula. By using the given information, the percentage loss of energy can be determined.

Formula used:
The percentage loss of the kinetic energy,
$\% {\text{loss in K}}{\text{.E = }}\left( {1 - {e^2}} \right) \times 100$
Where, $e$ is the coefficient of the restitution.

Complete step by step answer:
Given that,
The coefficient of the restitution, $e = 0.5$
The expression for finding percentage loss of the kinetic energy,
$\% {\text{loss in K}}{\text{.E = }}\left( {1 - {e^2}} \right) \times 100\,.............\left( 1 \right)$
By substituting the coefficient of the restitution in the equation (1), then then equation (1) is written as,
$\% {\text{loss in K}}{\text{.E = }}\left( {1 - {{\left( {0.5} \right)}^2}} \right) \times 100$
On squaring the term inside the bracket, then the above equation is written as,
$\% {\text{loss in K}}{\text{.E = }}\left( {1 - 0.25} \right) \times 100$
Now subtracting the term inside the bracket, then the above equation is written as,
$\% {\text{loss in K}}{\text{.E = 0}}{\text{.75}} \times 100$
On multiplying the above equation, then the above equation is written as,
$\% {\text{loss in K.E}}{{ = 75\% }}$
Thus, the above equation shows the percentage loss of energy on each rebounding of a ball dropped from a height.

Hence, the option (D) is the correct answer.

Note:
At each time the ball bounces, the height of the ball will reduce, it is very clear that the coefficient of restitution will depend on the height of the bouncing object. The coefficient of the restitution will be affected by the impact velocity, size, and shape of the colliding object.