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A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision is
- a)1 : 7
- b)3 : 4
- c)3 : 1
- d)1 : 4
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A ball A moving with certain velocity collides head on with another b...
mv = mv1 + mv2
v = v1 + v2
∴ 4v2 – 4v1
= 3v 4v2 – 4v1 = 3(v1 + v2)
v2 = 7v1
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A ball A moving with certain velocity collides head on with another b...
Introduction:
In this problem, we are given that a ball A moving with a certain velocity collides head-on with another body B of the same mass, which is at rest. We are also given the coefficient of restitution, which is a measure of how elastic the collision is. We need to find the ratio of the velocities of A and B after the collision.
Explanation:
To solve this problem, we can use the concept of conservation of momentum and the equation for the coefficient of restitution.
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
Mass of A * Velocity of A (before collision) + Mass of B * Velocity of B (before collision) = Mass of A * Velocity of A (after collision) + Mass of B * Velocity of B (after collision)
Since both bodies have the same mass, we can simplify the equation to:
Velocity of A (before collision) + Velocity of B (before collision) = Velocity of A (after collision) + Velocity of B (after collision)
Coefficient of Restitution:
The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. Mathematically, it can be expressed as:
e = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
Given that the coefficient of restitution is 3/4, we can substitute this value into the equation:
3/4 = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
Solving the Equations:
Now, we have two equations:
Velocity of A (before collision) + Velocity of B (before collision) = Velocity of A (after collision) + Velocity of B (after collision)
3/4 = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
We can solve these equations simultaneously to find the ratio of the velocities of A and B after the collision.
Conclusion:
After solving the equations, we find that the ratio of the velocities of A and B after the collision is 1:7, which corresponds to option A.
In this problem, we are given that a ball A moving with a certain velocity collides head-on with another body B of the same mass, which is at rest. We are also given the coefficient of restitution, which is a measure of how elastic the collision is. We need to find the ratio of the velocities of A and B after the collision.
Explanation:
To solve this problem, we can use the concept of conservation of momentum and the equation for the coefficient of restitution.
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
Mass of A * Velocity of A (before collision) + Mass of B * Velocity of B (before collision) = Mass of A * Velocity of A (after collision) + Mass of B * Velocity of B (after collision)
Since both bodies have the same mass, we can simplify the equation to:
Velocity of A (before collision) + Velocity of B (before collision) = Velocity of A (after collision) + Velocity of B (after collision)
Coefficient of Restitution:
The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. Mathematically, it can be expressed as:
e = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
Given that the coefficient of restitution is 3/4, we can substitute this value into the equation:
3/4 = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
Solving the Equations:
Now, we have two equations:
Velocity of A (before collision) + Velocity of B (before collision) = Velocity of A (after collision) + Velocity of B (after collision)
3/4 = (Velocity of B (after collision) - Velocity of A (after collision)) / (Velocity of A (before collision) - Velocity of B (before collision))
We can solve these equations simultaneously to find the ratio of the velocities of A and B after the collision.
Conclusion:
After solving the equations, we find that the ratio of the velocities of A and B after the collision is 1:7, which corresponds to option A.
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A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer?
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A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer?.
A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball A moving with certain velocity collides head on with another body B of the same mass at rest. If the coefficient of restitution is 3/4. The ratio of velocity A and B after collision isa)1 : 7b)3 : 4c)3 : 1d)1 : 4Correct answer is option 'A'. Can you explain this answer?.
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