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A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is
- a)0.6
- b)0.1
- c)0.01
- d)0
Correct answer is option 'D'. Can you explain this answer?
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Collision of two masses
We have two masses, m1 and m2, where m1 is travelling with a uniform velocity of 5 m/s along a line and m2 is stationary.
Collision occurs
When the two masses collide, there is a transfer of momentum between them. We can use the conservation of momentum principle to determine the velocity of the two masses after the collision.
Conservation of momentum
According to the conservation of momentum principle, the total momentum of the system before and after the collision should be the same. Mathematically, we can write:
m1v1 + m2v2 = (m1 + m2)v
where v1 and v2 are the velocities of m1 and m2 before the collision, v is the velocity of the combined masses after the collision, and m1 and m2 are the masses of the two objects.
Solving for v, we get:
v = (m1v1 + m2v2)/(m1 + m2)
Coefficient of restitution
The coefficient of restitution is a measure of the elasticity of the collision. It is a ratio of the relative velocity of separation to the relative velocity of approach between two objects after they collide.
Mathematically, we can write:
e = (v2' - v1')/(v1 - v2)
where e is the coefficient of restitution, v1 and v2 are the velocities of the two objects before the collision, and v1' and v2' are the velocities of the two objects after the collision.
In this case, since both masses travel together with the same velocity after the collision, v1' = v2' = v. Therefore, the coefficient of restitution can be written as:
e = (v - v1)/(v1 - 0)
where v1 is the velocity of m1 before the collision.
Solving for e, we get:
e = 0
Therefore, the correct answer is option D, 0.
We have two masses, m1 and m2, where m1 is travelling with a uniform velocity of 5 m/s along a line and m2 is stationary.
Collision occurs
When the two masses collide, there is a transfer of momentum between them. We can use the conservation of momentum principle to determine the velocity of the two masses after the collision.
Conservation of momentum
According to the conservation of momentum principle, the total momentum of the system before and after the collision should be the same. Mathematically, we can write:
m1v1 + m2v2 = (m1 + m2)v
where v1 and v2 are the velocities of m1 and m2 before the collision, v is the velocity of the combined masses after the collision, and m1 and m2 are the masses of the two objects.
Solving for v, we get:
v = (m1v1 + m2v2)/(m1 + m2)
Coefficient of restitution
The coefficient of restitution is a measure of the elasticity of the collision. It is a ratio of the relative velocity of separation to the relative velocity of approach between two objects after they collide.
Mathematically, we can write:
e = (v2' - v1')/(v1 - v2)
where e is the coefficient of restitution, v1 and v2 are the velocities of the two objects before the collision, and v1' and v2' are the velocities of the two objects after the collision.
In this case, since both masses travel together with the same velocity after the collision, v1' = v2' = v. Therefore, the coefficient of restitution can be written as:
e = (v - v1)/(v1 - 0)
where v1 is the velocity of m1 before the collision.
Solving for e, we get:
e = 0
Therefore, the correct answer is option D, 0.
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A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer?
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A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer?.
A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer?.
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A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A mass 1 m of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with astationary mass m2 of 1000 kg. After the collision, both the masses travel together with thesame velocity. The coefficient of restitution isa)0.6b)0.1c)0.01d)0Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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