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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?
[JEE 2010]
- a)Total momentum of the system is 3 kg ms-1
- b)Momentum of 5 kg mass after collision is 4 kg ms-1
- c)Kinetic energy of the centre of mass is 0.75 J
- d)Total kinetic energy of the system is 4 J
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
A point mass of 1 kg collides elastically with a stationary point mass...
By using the conservation of linear momentum
Also, the total momentum is 3 kg m/s
Also, the total momentum is 3 kg m/s
Most Upvoted Answer
A point mass of 1 kg collides elastically with a stationary point mass...
Explanation:
Conservation of momentum:
- In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
- The momentum of an object is given by the product of its mass and velocity.
Initial momentum:
- The initial momentum of the system is the sum of the momenta of the two masses before the collision.
- The 1 kg mass is moving towards the stationary 5 kg mass, so its initial momentum is (1 kg) * (-2 m/s) = -2 kg m/s.
- The initial momentum of the 5 kg mass is 0 kg m/s since it is stationary.
Final momentum:
- After the collision, the 1 kg mass reverses its direction and moves with a velocity of 2 m/s.
- The final momentum of the 1 kg mass is (1 kg) * (2 m/s) = 2 kg m/s in the opposite direction.
- The final momentum of the 5 kg mass is calculated using the conservation of momentum.
- Let the final velocity of the 5 kg mass be v m/s.
- The initial momentum of the system is equal to the final momentum of the system.
- (-2 kg m/s) + (0 kg m/s) = (1 kg) * (2 m/s) + (5 kg) * v
- -2 = 2 + 5v
- 5v = -4
- v = -4/5 m/s
- The final momentum of the 5 kg mass is (5 kg) * (-4/5 m/s) = -4 kg m/s.
Answering the statements:
a) Total momentum of the system is 3 kg m/s.
- The initial momentum of the system is -2 kg m/s and the final momentum is 2 kg m/s + (-4 kg m/s) = -2 kg m/s.
- The total momentum is conserved, so the statement is incorrect.
b) Momentum of 5 kg mass after collision is 4 kg m/s.
- The final momentum of the 5 kg mass is -4 kg m/s, so the statement is incorrect.
c) Kinetic energy of the centre of mass is 0.75 J.
- The kinetic energy of the centre of mass is given by the formula KE = (1/2) * total mass * (velocity of centre of mass)^2.
- The total mass is 1 kg + 5 kg = 6 kg.
- The velocity of the centre of mass is the average of the velocities of the two masses, which is (2 m/s + 0 m/s)/2 = 1 m/s.
- Plugging these values into the formula, KE = (1/2) * 6 kg * (1 m/s)^2 = 3 J.
- The statement is incorrect.
d) Total kinetic energy of the system is 4 J.
- The initial kinetic energy of the system is (1/2) * (1 kg) * (-2 m/s)^2 + (1/2) * (5 kg) * (0 m/s)^2 = 2 J.
- The final kinetic energy of the system is (1/2) * (1 kg) * (2 m/s)^2 + (1/2
Conservation of momentum:
- In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
- The momentum of an object is given by the product of its mass and velocity.
Initial momentum:
- The initial momentum of the system is the sum of the momenta of the two masses before the collision.
- The 1 kg mass is moving towards the stationary 5 kg mass, so its initial momentum is (1 kg) * (-2 m/s) = -2 kg m/s.
- The initial momentum of the 5 kg mass is 0 kg m/s since it is stationary.
Final momentum:
- After the collision, the 1 kg mass reverses its direction and moves with a velocity of 2 m/s.
- The final momentum of the 1 kg mass is (1 kg) * (2 m/s) = 2 kg m/s in the opposite direction.
- The final momentum of the 5 kg mass is calculated using the conservation of momentum.
- Let the final velocity of the 5 kg mass be v m/s.
- The initial momentum of the system is equal to the final momentum of the system.
- (-2 kg m/s) + (0 kg m/s) = (1 kg) * (2 m/s) + (5 kg) * v
- -2 = 2 + 5v
- 5v = -4
- v = -4/5 m/s
- The final momentum of the 5 kg mass is (5 kg) * (-4/5 m/s) = -4 kg m/s.
Answering the statements:
a) Total momentum of the system is 3 kg m/s.
- The initial momentum of the system is -2 kg m/s and the final momentum is 2 kg m/s + (-4 kg m/s) = -2 kg m/s.
- The total momentum is conserved, so the statement is incorrect.
b) Momentum of 5 kg mass after collision is 4 kg m/s.
- The final momentum of the 5 kg mass is -4 kg m/s, so the statement is incorrect.
c) Kinetic energy of the centre of mass is 0.75 J.
- The kinetic energy of the centre of mass is given by the formula KE = (1/2) * total mass * (velocity of centre of mass)^2.
- The total mass is 1 kg + 5 kg = 6 kg.
- The velocity of the centre of mass is the average of the velocities of the two masses, which is (2 m/s + 0 m/s)/2 = 1 m/s.
- Plugging these values into the formula, KE = (1/2) * 6 kg * (1 m/s)^2 = 3 J.
- The statement is incorrect.
d) Total kinetic energy of the system is 4 J.
- The initial kinetic energy of the system is (1/2) * (1 kg) * (-2 m/s)^2 + (1/2) * (5 kg) * (0 m/s)^2 = 2 J.
- The final kinetic energy of the system is (1/2) * (1 kg) * (2 m/s)^2 + (1/2
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A point mass of 1 kg collides elastically with a stationary point mass...
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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer?
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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer?.
A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer?.
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ample number of questions to practice A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms-1. Which of the following statement(s) is (are ) correct for the system of these two masses ?[JEE 2010]a)Total momentum of the system is 3 kg ms-1b)Momentum of 5 kg mass after collision is 4 kg ms-1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4 JCorrect answer is option 'A,C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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