A ball is dropped from a height of 10 m. It strikes the ground and rebounds up to a height of 2.5 m. During the collision, the per cent loss in the kinetic energy is:
- A.100%
- B.25%
- C.50%
- D.75%
Correct answer
Explanation
The correct answer is D, 75%. The ball falls from 10 m but rises back only 2.5 m, so it keeps one quarter of its energy and loses three quarters. Just before the ball hits the ground, its kinetic energy equals the potential energy it had at the top, that is mgh with h = 10 m. Just after the bounce, the kinetic energy is only as much as is needed to lift it 2.5 m, so it is mg multiplied by 2.5. The ratio is 2.5 divided by 10, which is one fourth, so 25 per cent of the kinetic energy is left and 75 per cent is lost as heat and sound during the collision. The mass cancels out, so the heights alone decide the answer. Option A is wrong because the ball does rebound, so all the energy is not lost. Option B is wrong because 25 per cent is the energy kept, not the energy lost. Option C is wrong because losing half the energy would take the ball back to 5 m. Exam tip: in a bounce, percentage loss equals (1 minus h2 by h1) multiplied by 100.
Practice Questions
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