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A ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?
- a)1 : 7
- b)6 : 7
- c)1 : 6
- d)6 : 1
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A ball of mass m, moving with a constant velocity, collides with anoth...
Given Data:
- Mass of each ball, m
- Coefficient of restitution, e = 5/7
- Initial velocity of the first ball, u1 = v
- Initial velocity of the second ball, u2 = 0
- Final velocity of the first ball, v1
- Final velocity of the second ball, v2
Using the formula for coefficient of restitution:
e = (Relative velocity of separation) / (Relative velocity of approach)
5/7 = (v2 - v1) / (u1 - u2)
5/7 = (v2 - v1) / v
As the first ball collides with the second ball:
- Momentum is conserved.
- Initial momentum = Final momentum
- m * u1 = m * v1 + m * v2
- v = v1 + v2
Substitute v = v1 + v2 in the equation 5/7 = (v2 - v1) / v:
5/7 = (v2 - v1) / (v1 + v2)
5(v1 + v2) = 7(v2 - v1)
5v1 + 5v2 = 7v2 - 7v1
12v1 = 2v2
v1 / v2 = 1 / 6
Therefore, the ratio of v1 : v2 is 1 : 6. Hence, option C is correct.
- Mass of each ball, m
- Coefficient of restitution, e = 5/7
- Initial velocity of the first ball, u1 = v
- Initial velocity of the second ball, u2 = 0
- Final velocity of the first ball, v1
- Final velocity of the second ball, v2
Using the formula for coefficient of restitution:
e = (Relative velocity of separation) / (Relative velocity of approach)
5/7 = (v2 - v1) / (u1 - u2)
5/7 = (v2 - v1) / v
As the first ball collides with the second ball:
- Momentum is conserved.
- Initial momentum = Final momentum
- m * u1 = m * v1 + m * v2
- v = v1 + v2
Substitute v = v1 + v2 in the equation 5/7 = (v2 - v1) / v:
5/7 = (v2 - v1) / (v1 + v2)
5(v1 + v2) = 7(v2 - v1)
5v1 + 5v2 = 7v2 - 7v1
12v1 = 2v2
v1 / v2 = 1 / 6
Therefore, the ratio of v1 : v2 is 1 : 6. Hence, option C is correct.
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Community Answer
A ball of mass m, moving with a constant velocity, collides with anoth...
Let the velocity of the ball before the collision be u.
Velocity of the bodies after the collision is given by:
Using conservation of momentum
mu = mv1 + mv2
u = v1 + v2
Coefficient of restitution,
Hence,
Therefore, the ratio of velocities is given by:
Therefore, it is the correct option.
Velocity of the bodies after the collision is given by:
Using conservation of momentum
mu = mv1 + mv2
u = v1 + v2
Coefficient of restitution,
Hence,
Therefore, the ratio of velocities is given by:
Therefore, it is the correct option.
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A ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. Can you explain this answer?
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A ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. 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 ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. 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 ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. Can you explain this answer?.
A ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. 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 ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. 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 ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice A ball of mass m, moving with a constant velocity, collides with another identical ball at rest. After the collision, the first ball acquires velocity v1 and the second ball that was at rest before collision acquires velocity v2. If the coefficient of restitution is given to be 5/7, what will be the ratio v1 : v2?a)1 : 7b)6 : 7c)1 : 6d)6 : 1Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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