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Head-on elastic collision with a body at rest: velocities, mass ratio or energy transferred

This type of question, asked 4 times: 2021 Paper 10, 2021 Paper 25, 27 Jun 2022, 25 Jan 2023. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 10

    2
    An object of mass m1m_{1} collides with another object of mass m2m_{2}, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2:m1m_{2}:m_{1} is:

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  2. Question 2

    2021 Paper 25

    12
    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Body ' PP ' having mass MM moving with speed ' uu ' has head-on collision elastically with another body ' QQ ' having mass ' mm ' initially at rest. If m<<Mm < < M, body ' QQ ' will have a maximum speed equal to ' 2u2u ' after collision. Reason R: During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

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  3. Question 3

    27 Jun 2022

    8
    What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

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  4. Question 4

    25 Jan 2023

    115
    A body of mass 1 kg1\text{ }kg collides head on elastically with a stationary body of mass 3 kg3\text{ }kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 ms\frac{2\text{ }m}{s}. The initial speed of the smaller body before collision is ____\_\_\_\_ ms−1ms^{- 1}.