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:
- 7.5 m
- 10 m
- 2.5 m
- 5 m
The Correct Option is D
Solution and Explanation
1. Initial Potential Energy: Initial potential energy (PE) = mgh, where m is the mass, g is acceleration due to gravity, and h is the initial height (10 m).
2. Kinetic Energy Just Before Impact: By conservation of energy, the potential energy is converted to kinetic energy (KE) just before the object strikes the ground: KE = mgh.
3. Kinetic Energy After Impact: The object loses 50% of its KE after striking the ground, so the remaining KE is 0.5(mgh).
4. Rebound Height: The remaining KE is converted back to potential energy as the object rebounds. Let h’ be the rebound height. 0.5(mgh) = mgh’ h’ = 0.5h = 0.5(10 m) = 5 m
5. Conclusion: The rebound height is 5 m.
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