Question

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:

• A. 7.5 m
• B. 10 m
• C. 2.5 m
• D. 5 m

Answer 1

The Correct Option is D

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.