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A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision is
- a)30o
- b)45o
- c)60o
- d)90o
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A sphere has a perfectly elastic oblique collision with another identi...
Law of conservation of momentum gives
mu1 = mv1cosq1 + mv2cosq2 .......(1)
and 0 mv1sinq1 - mv2sinq1 ....(2)
Energy conservation gives
....(3)
Squaring and adding (1) and (2) and comparing with (3) we get θ1 + θ2 = 90o
mu1 = mv1cosq1 + mv2cosq2 .......(1)
and 0 mv1sinq1 - mv2sinq1 ....(2)
Energy conservation gives
....(3)Squaring and adding (1) and (2) and comparing with (3) we get θ1 + θ2 = 90o
Most Upvoted Answer
A sphere has a perfectly elastic oblique collision with another identi...
Law of conservation of momentum gives
mu1 = mv1cosq1 + mv2cosq2 .......(1)
and 0 mv1sinq1 - mv2sinq1 ....(2)
Energy conservation gives
....(3)
Squaring and adding (1) and (2) and comparing with (3) we get θ1 + θ2 = 90o
mu1 = mv1cosq1 + mv2cosq2 .......(1)
and 0 mv1sinq1 - mv2sinq1 ....(2)
Energy conservation gives
....(3)Squaring and adding (1) and (2) and comparing with (3) we get θ1 + θ2 = 90o
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Community Answer
A sphere has a perfectly elastic oblique collision with another identi...
Explanation:
1. Elastic collision:
In an elastic collision, both the momentum and kinetic energy of the system are conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
2. Oblique collision:
An oblique collision refers to a collision where the two objects are moving at an angle to each other before the collision.
3. Identical spheres:
Since the spheres are identical, they have the same mass and radius.
4. Initial conditions:
One of the spheres is initially at rest, while the other sphere is moving with a certain velocity. Let's call the sphere that is initially at rest as Sphere A and the moving sphere as Sphere B.
5. Conservation of momentum:
Since the collision is elastic, the total momentum before the collision is equal to the total momentum after the collision. Since Sphere A is initially at rest, its initial momentum is zero. Therefore, the total momentum before the collision is equal to the momentum of Sphere B.
6. Angle between velocities:
After the collision, let's assume that the angle between the velocities of Sphere A and Sphere B is θ. Since the spheres are identical, the magnitude of their velocities will be the same.
7. Conservation of kinetic energy:
Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Since Sphere A is initially at rest, its initial kinetic energy is zero. Therefore, the total kinetic energy before the collision is equal to the kinetic energy of Sphere B.
8. Final velocities:
Since the spheres have the same mass and the same final kinetic energy, their final velocities will be the same. This means that the angle between their velocities after the collision is 90 degrees (option D).
Conclusion:
In a perfectly elastic oblique collision between two identical spheres, the angle between their velocities after the collision is 90 degrees.
1. Elastic collision:
In an elastic collision, both the momentum and kinetic energy of the system are conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
2. Oblique collision:
An oblique collision refers to a collision where the two objects are moving at an angle to each other before the collision.
3. Identical spheres:
Since the spheres are identical, they have the same mass and radius.
4. Initial conditions:
One of the spheres is initially at rest, while the other sphere is moving with a certain velocity. Let's call the sphere that is initially at rest as Sphere A and the moving sphere as Sphere B.
5. Conservation of momentum:
Since the collision is elastic, the total momentum before the collision is equal to the total momentum after the collision. Since Sphere A is initially at rest, its initial momentum is zero. Therefore, the total momentum before the collision is equal to the momentum of Sphere B.
6. Angle between velocities:
After the collision, let's assume that the angle between the velocities of Sphere A and Sphere B is θ. Since the spheres are identical, the magnitude of their velocities will be the same.
7. Conservation of kinetic energy:
Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Since Sphere A is initially at rest, its initial kinetic energy is zero. Therefore, the total kinetic energy before the collision is equal to the kinetic energy of Sphere B.
8. Final velocities:
Since the spheres have the same mass and the same final kinetic energy, their final velocities will be the same. This means that the angle between their velocities after the collision is 90 degrees (option D).
Conclusion:
In a perfectly elastic oblique collision between two identical spheres, the angle between their velocities after the collision is 90 degrees.
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A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision isa)30ob)45oc)60od)90oCorrect answer is option 'D'. Can you explain this answer?
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A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision isa)30ob)45oc)60od)90oCorrect answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision isa)30ob)45oc)60od)90oCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision isa)30ob)45oc)60od)90oCorrect answer is option 'D'. Can you explain this answer?.
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