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A body falling form a height of 10 m rebounds from hard floor. if it loses 20% energy in the impact, then coefficient of restitution is
- a)0.89
- b)0.56
- c)0.23
- d)0.18
Correct answer is option 'A'. Can you explain this answer?
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A body falling form a height of 10 m rebounds from hard floor. if it l...
Understanding the Problem
A body falls from a height of 10 m and loses 20% of its energy upon impact with a hard floor. We need to determine the coefficient of restitution (e).
Key Concepts
- Potential Energy (PE): When the body is at a height (h), it has potential energy given by PE = mgh, where g is the acceleration due to gravity (approximately 9.81 m/s²).
- Kinetic Energy (KE): Just before impact, all potential energy converts to kinetic energy. Thus, KE = PE at the moment before impact.
- Coefficient of Restitution (e): It is defined as the ratio of the speed after the impact to the speed before the impact. It can also be related to the energies:
e = sqrt(KE_after / KE_before)
Calculating Initial Potential Energy
- Height (h) = 10 m
- Initial PE = mgh = mg(10)
Calculating Energy Loss
- If 20% energy is lost, then 80% of the energy is retained.
- KE_before = Initial PE = mg(10)
- KE_after = 80% of KE_before = 0.80 * mg(10)
Finding the Coefficient of Restitution
- Using the formula for the coefficient of restitution:
e = sqrt(KE_after / KE_before)
- Plugging in the values:
e = sqrt(0.80 * mg(10) / mg(10)) = sqrt(0.80)
- Thus, e = sqrt(0.80) ≈ 0.89
Conclusion
The coefficient of restitution is approximately 0.89, confirming that the correct answer is option 'A'.
A body falls from a height of 10 m and loses 20% of its energy upon impact with a hard floor. We need to determine the coefficient of restitution (e).
Key Concepts
- Potential Energy (PE): When the body is at a height (h), it has potential energy given by PE = mgh, where g is the acceleration due to gravity (approximately 9.81 m/s²).
- Kinetic Energy (KE): Just before impact, all potential energy converts to kinetic energy. Thus, KE = PE at the moment before impact.
- Coefficient of Restitution (e): It is defined as the ratio of the speed after the impact to the speed before the impact. It can also be related to the energies:
e = sqrt(KE_after / KE_before)
Calculating Initial Potential Energy
- Height (h) = 10 m
- Initial PE = mgh = mg(10)
Calculating Energy Loss
- If 20% energy is lost, then 80% of the energy is retained.
- KE_before = Initial PE = mg(10)
- KE_after = 80% of KE_before = 0.80 * mg(10)
Finding the Coefficient of Restitution
- Using the formula for the coefficient of restitution:
e = sqrt(KE_after / KE_before)
- Plugging in the values:
e = sqrt(0.80 * mg(10) / mg(10)) = sqrt(0.80)
- Thus, e = sqrt(0.80) ≈ 0.89
Conclusion
The coefficient of restitution is approximately 0.89, confirming that the correct answer is option 'A'.
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A body falling form a height of 10 m rebounds from hard floor. if it loses 20% energy in the impact, then coefficient of restitution isa)0.89b)0.56c)0.23d)0.18Correct answer is option 'A'. Can you explain this answer?
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A body falling form a height of 10 m rebounds from hard floor. if it loses 20% energy in the impact, then coefficient of restitution isa)0.89b)0.56c)0.23d)0.18Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body falling form a height of 10 m rebounds from hard floor. if it loses 20% energy in the impact, then coefficient of restitution isa)0.89b)0.56c)0.23d)0.18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body falling form a height of 10 m rebounds from hard floor. if it loses 20% energy in the impact, then coefficient of restitution isa)0.89b)0.56c)0.23d)0.18Correct answer is option 'A'. Can you explain this answer?.
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