Coefficient Of Restitution
A rubber ball is dropped from a height of 2 m onto a hard floor and rebounds to a height of 1.28 m after the first bounce. What is the coefficient of restitution between the ball and the floor?
Select the correct option:
Solution
0.8
As discussed in NCERT Class 11, Chapter 6 (Work, Energy and Power), the coefficient of restitution between a falling object and a fixed surface equals the ratio of the rebound speed to the impact speed. Using energy conservation, speed is proportional to the square root of the drop or rebound height, so e = sqrt(h_rebound / h_drop) = sqrt(1.28 / 2) = sqrt(0.64) = 0.8. The coefficient lies between 0 and 1 for a real bounce, with 1 being perfectly elastic. The option 0.64 mistakenly takes the height ratio itself without the square root. The option 0.9 overestimates the bounce. The option 0.5 underestimates it. A plausibility check: the ball loses energy on impact, so the rebound height of 1.28 m is less than the 2 m drop, giving e below 1, and the value 0.8 fits a fairly bouncy but non-ideal rubber ball.
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- coefficient of restitution
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
0.8
As discussed in NCERT Class 11, Chapter 6 (Work, Energy and Power), the coefficient of restitution between a falling object and a fixed surface equals the ratio of the rebound speed to the impact speed. Using energy conservation, speed is proportional to the square root of the drop or rebound height, so e = sqrt(h_rebound / h_drop) = sqrt(1.28 / 2) = sqrt(0.64) = 0.8. The coefficient lies between 0 and 1 for a real bounce, with 1 being perfectly elastic. The option 0.64 mistakenly takes the height ratio itself without the square root. The option 0.9 overestimates the bounce. The option 0.5 underestimates it. A plausibility check: the ball loses energy on impact, so the rebound height of 1.28 m is less than the 2 m drop, giving e below 1, and the value 0.8 fits a fairly bouncy but non-ideal rubber ball.
This hard difficulty physics question is from the chapter work, energy and power, covering the topic of coefficient of restitution. It appeared in the 2025 exam.
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