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A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor is
- a)0.5 m
- b)0.75 m
- c)1.0 m
- d)1.5 m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A Particle is dropped from a height of 3 m on a horizantal floor, whic...
Given:
- Initial height of the particle = 3 m
- Coefficient of restitution of the ball with the floor = 1/2
To find:
- The height to which the ball will rebound after striking the floor
Explanation:
1. Coefficient of restitution:
The coefficient of restitution (e) is a measure of the ability of a ball to bounce back after a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding bodies.
Mathematically, e = (v2f - v1f) / (v1i - v2i)
Where,
- v1i and v2i are the initial velocities of the two bodies before collision
- v1f and v2f are the final velocities of the two bodies after collision
In this case, the ball is dropped from a height, so its initial velocity is zero.
2. Calculation:
When the ball is dropped from a height of 3 m, it falls freely under the influence of gravity. As it hits the floor, it comes to a stop momentarily and then rebounds.
The rebound height can be calculated using the equation:
h = e^2 * H
Where,
- h is the rebound height
- e is the coefficient of restitution
- H is the initial height
Substituting the given values:
h = (1/2)^2 * 3
h = 1/4 * 3
h = 3/4
h = 0.75 m
3. Answer:
The height to which the ball will rebound after striking the floor is 0.75 m. Therefore, the correct answer is option B.
- Initial height of the particle = 3 m
- Coefficient of restitution of the ball with the floor = 1/2
To find:
- The height to which the ball will rebound after striking the floor
Explanation:
1. Coefficient of restitution:
The coefficient of restitution (e) is a measure of the ability of a ball to bounce back after a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding bodies.
Mathematically, e = (v2f - v1f) / (v1i - v2i)
Where,
- v1i and v2i are the initial velocities of the two bodies before collision
- v1f and v2f are the final velocities of the two bodies after collision
In this case, the ball is dropped from a height, so its initial velocity is zero.
2. Calculation:
When the ball is dropped from a height of 3 m, it falls freely under the influence of gravity. As it hits the floor, it comes to a stop momentarily and then rebounds.
The rebound height can be calculated using the equation:
h = e^2 * H
Where,
- h is the rebound height
- e is the coefficient of restitution
- H is the initial height
Substituting the given values:
h = (1/2)^2 * 3
h = 1/4 * 3
h = 3/4
h = 0.75 m
3. Answer:
The height to which the ball will rebound after striking the floor is 0.75 m. Therefore, the correct answer is option B.
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Community Answer
A Particle is dropped from a height of 3 m on a horizantal floor, whic...
If a ball is dropped from a height ho on a horizontal floor, then it strikes with the floor with a speed,
and it rebounds from the floor with a speed,
Where, Coefficient of restitution =
First height of rebound,
Therefore,
The velocity of ball after nth rebound; Vn = enVo
The height of ball after nth rebound, hn = e2nho
Calculation:
Given: ho = 3 m., e = 0.5, h1 = ?
We know that, height after first rebound:
h1 = (0.5)2 × 3 = 0.75 m.
The height of ball after nth rebound, hn = e2nho
Calculation:
Given: ho = 3 m., e = 0.5, h1 = ?
We know that, height after first rebound:
h1 = (0.5)2 × 3 = 0.75 m.
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A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer?
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A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer?.
A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Particle is dropped from a height of 3 m on a horizantal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the hall will rebound after striking the floor isa)0.5 mb)0.75 mc)1.0 md)1.5 mCorrect answer is option 'B'. Can you explain this answer?.
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