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Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.
What is the coefficient of restitution?
- a)c/4 - 1
- b)1.5 c - 1
- c)2.5 c - 1.5
- d)c/3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Spheres A and B of equal radius and of masses 2 m and m, respectively,...
Magnitude of the Impulse received | ΔI| = 4mcu
V1 and V2 are velocities after collision.
Magnitude of impulse is the same on both A and B.
For body A:
2mv1 - 6mu = -4mcu
2mv1 = 6mu - 4cum
V1 = 3u - 2cu(→)
For body B:
mv2 - (-mu) = 4mcu
mv2 = 4mcu - mu
v2 = 4cu - u(→) - speed of B
Magnitude of impulse is the same on both A and B.
For body A:
2mv1 - 6mu = -4mcu
2mv1 = 6mu - 4cum
V1 = 3u - 2cu(→)
For body B:
mv2 - (-mu) = 4mcu
mv2 = 4mcu - mu
v2 = 4cu - u(→) - speed of B
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Community Answer
Spheres A and B of equal radius and of masses 2 m and m, respectively,...
Given data:
- Mass of sphere A = 2m
- Mass of sphere B = m
- Initial speed of A = 3u
- Initial speed of B = u
- Impulse experienced by B = 4mcu
Calculation:
1. Conservation of momentum:
- Initial momentum = 2m * 3u + m * u = 7mu
- Final momentum = (2m + m) * V + 4mcu (as impulse is experienced by B)
- According to conservation of momentum, initial momentum = final momentum
- 7mu = 3mV + 4mcu
- V = (7u - 4cu) / 3
2. Coefficient of restitution (e):
- e = (Final relative velocity of separation) / (Initial relative velocity of approach)
- Final relative velocity = V
- Initial relative velocity = 3u + u = 4u
- e = V / 4u
- Substitute the value of V from above calculation
- e = (7u - 4cu) / (3 * 4u) = (7/12 - c/3)
Final answer:
- The coefficient of restitution (e) = 7/12 - c/3
- Simplifying, we get e = 1.5c - 1
Therefore, the correct answer is option B) 1.5c - 1.
- Mass of sphere A = 2m
- Mass of sphere B = m
- Initial speed of A = 3u
- Initial speed of B = u
- Impulse experienced by B = 4mcu
Calculation:
1. Conservation of momentum:
- Initial momentum = 2m * 3u + m * u = 7mu
- Final momentum = (2m + m) * V + 4mcu (as impulse is experienced by B)
- According to conservation of momentum, initial momentum = final momentum
- 7mu = 3mV + 4mcu
- V = (7u - 4cu) / 3
2. Coefficient of restitution (e):
- e = (Final relative velocity of separation) / (Initial relative velocity of approach)
- Final relative velocity = V
- Initial relative velocity = 3u + u = 4u
- e = V / 4u
- Substitute the value of V from above calculation
- e = (7u - 4cu) / (3 * 4u) = (7/12 - c/3)
Final answer:
- The coefficient of restitution (e) = 7/12 - c/3
- Simplifying, we get e = 1.5c - 1
Therefore, the correct answer is option B) 1.5c - 1.
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Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer?
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Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. 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 Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer?.
Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. 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 Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer?.
Solutions for Spheres A and B of equal radius and of masses 2 m and m, respectively, are moving towards each other and strike directly. The speeds of A and B before the collision are 3u and u, respectively. The collision is such that B experiences an impulse of 4mcu, where c is constant.What is the coefficient of restitution?a)c/4 - 1b)1.5 c - 1c)2.5 c - 1.5d)c/3Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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