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Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction?
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Given:
- Mass of sphere A = m1
- Mass of sphere B = m2
- Sphere A is at rest initially
- Sphere B is moving with velocity v along x-axis
- After collision, sphere B has velocity v/2 in a direction perpendicular to the original direction
To find:
- Direction in which sphere A moves after collision
Solution:
Conservation of Momentum:
- Before collision, the momentum of the system is given by: P1 = m2v (since sphere A is at rest)
- After collision, the momentum of the system is given by: P2 = m1u1 + m2u2 (where u1 and u2 are the velocities of spheres A and B after collision, respectively)
- According to the law of conservation of momentum, P1 = P2
- Therefore, m2v = m1u1 + m2u2
Conservation of Kinetic Energy:
- Before collision, the kinetic energy of the system is given by: KE1 = (1/2)m2v^2
- After collision, the kinetic energy of the system is given by: KE2 = (1/2)m1u1^2 + (1/2)m2u2^2
- According to the law of conservation of kinetic energy, KE1 = KE2
- Therefore, (1/2)m2v^2 = (1/2)m1u1^2 + (1/2)m2u2^2
Calculations:
- From the first equation of conservation of momentum, we get: u2 = (m2v - m1u1)/m2
- Substituting this value of u2 in the equation of conservation of kinetic energy, we get:
(1/2)m2v^2 = (1/2)m1u1^2 + (1/2)m2(m2v - m1u1)^2/m2^2
- Simplifying this equation, we get: u1 = v/3
Direction of Sphere A:
- Since sphere B has a velocity of v/2 in a direction perpendicular to the original direction, the direction in which sphere A moves after collision is also perpendicular to the original direction
- Therefore, sphere A moves in the y-axis direction (i.e. upwards or downwards)
Answer:
- Sphere A moves in the y-axis direction (i.e. upwards or downwards) after collision.
- Mass of sphere A = m1
- Mass of sphere B = m2
- Sphere A is at rest initially
- Sphere B is moving with velocity v along x-axis
- After collision, sphere B has velocity v/2 in a direction perpendicular to the original direction
To find:
- Direction in which sphere A moves after collision
Solution:
Conservation of Momentum:
- Before collision, the momentum of the system is given by: P1 = m2v (since sphere A is at rest)
- After collision, the momentum of the system is given by: P2 = m1u1 + m2u2 (where u1 and u2 are the velocities of spheres A and B after collision, respectively)
- According to the law of conservation of momentum, P1 = P2
- Therefore, m2v = m1u1 + m2u2
Conservation of Kinetic Energy:
- Before collision, the kinetic energy of the system is given by: KE1 = (1/2)m2v^2
- After collision, the kinetic energy of the system is given by: KE2 = (1/2)m1u1^2 + (1/2)m2u2^2
- According to the law of conservation of kinetic energy, KE1 = KE2
- Therefore, (1/2)m2v^2 = (1/2)m1u1^2 + (1/2)m2u2^2
Calculations:
- From the first equation of conservation of momentum, we get: u2 = (m2v - m1u1)/m2
- Substituting this value of u2 in the equation of conservation of kinetic energy, we get:
(1/2)m2v^2 = (1/2)m1u1^2 + (1/2)m2(m2v - m1u1)^2/m2^2
- Simplifying this equation, we get: u1 = v/3
Direction of Sphere A:
- Since sphere B has a velocity of v/2 in a direction perpendicular to the original direction, the direction in which sphere A moves after collision is also perpendicular to the original direction
- Therefore, sphere A moves in the y-axis direction (i.e. upwards or downwards)
Answer:
- Sphere A moves in the y-axis direction (i.e. upwards or downwards) after collision.
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Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction?
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Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction?.
Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction?.
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