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A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is?
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A body of mass 5 kg make an elastic collision with another body at res...
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A body of mass 5 kg make an elastic collision with another body at res...
Given Data:
Mass of first body (m1) = 5 kg
Initial velocity of first body (u1) = u
Final velocity of first body (v1) = u/10
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
m1u1 = m1v1 + m2v2
5u = 5(u/10) + m2v2
5u = 0.5u + m2v2
4.5u = m2v2
Conservation of Kinetic Energy:
In an elastic collision, kinetic energy is conserved.
0.5m1u1^2 = 0.5m1v1^2 + 0.5m2v2^2
0.5(5u^2) = 0.5(5(u/10)^2) + 0.5(m2v2^2)
2.5u^2 = 0.25u^2 + 0.5(m2v2^2)
2.25u^2 = 0.5(m2v2^2)
Solving for m2:
From the conservation of momentum equation: 4.5u = m2v2
m2 = 4.5u/v2
Substitute m2 = 4.5u/v2 into the conservation of kinetic energy equation:
2.25u^2 = 0.5((4.5u/v2)v2)^2
2.25u^2 = 0.5(4.5u)^2
2.25u^2 = 10.125u^2
m2 = 10.125u^2 / 2.25u^2
m2 = 4.5 kg
Therefore, the mass of the second body is 4.5 kg.
Mass of first body (m1) = 5 kg
Initial velocity of first body (u1) = u
Final velocity of first body (v1) = u/10
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
m1u1 = m1v1 + m2v2
5u = 5(u/10) + m2v2
5u = 0.5u + m2v2
4.5u = m2v2
Conservation of Kinetic Energy:
In an elastic collision, kinetic energy is conserved.
0.5m1u1^2 = 0.5m1v1^2 + 0.5m2v2^2
0.5(5u^2) = 0.5(5(u/10)^2) + 0.5(m2v2^2)
2.5u^2 = 0.25u^2 + 0.5(m2v2^2)
2.25u^2 = 0.5(m2v2^2)
Solving for m2:
From the conservation of momentum equation: 4.5u = m2v2
m2 = 4.5u/v2
Substitute m2 = 4.5u/v2 into the conservation of kinetic energy equation:
2.25u^2 = 0.5((4.5u/v2)v2)^2
2.25u^2 = 0.5(4.5u)^2
2.25u^2 = 10.125u^2
m2 = 10.125u^2 / 2.25u^2
m2 = 4.5 kg
Therefore, the mass of the second body is 4.5 kg.
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A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is?
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A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is?.
A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 5 kg make an elastic collision with another body at rest and continue to move in the originna direction after collision with a velocity equal is 1/10th of the original velocity then mass of the second body is?.
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