An object falls from a height of 10 m above the ground. After striking the ground it loses 50% of its kinetic energy. The height upto which the object can rebound from the ground is: [2024]

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Solution

Q.
An object falls from a height of 10 m above the ground. After striking the ground it loses 50% of its kinetic energy. The height upto which the object can rebounce from the ground is: [2024]

1 7.5 m

2 10 m

3 2.5 m

4 5 m

Ans.
(4)

Given, height $(h) = 10 m$

$P.E. at h = 10 m,$ $P.E. = m g \times 10 = 10 m g$

Before striking ground,

${(K . E .)}_{i} = P.E. at h = 10$ $m = 10 m g$

After striking ground,

${(K . E .)}_{f} = 50 % {(K . E .)}_{i} = \frac{1}{2} \times 10 m g$

${(K . E .)}_{f} = 5 m g$

When object rebounces to $h',$

${(K . E .)}_{f} = P.E. at h'$

So, $5 m g = m g h' \Rightarrow h' = 5 m$

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