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A ball of mass m moving at a speed v mak...

A ball of mass m moving at a speed v makes a head on inelastic collision with an identical ball at rest. The kinetic energy of the balls after the collision is `3/4th` of the original. Find the coefficient of restitution.

Text Solution

Verified by Experts

The correct Answer is:
A, B
For the given conditons, we can use Eq. (xiv) or
`v_1^()'=((1+e)/(2))v` and `v_2^()'=((1-e)/(2))v`
Given that `K_f=3/4K_i`
or `1/2mv_1^()'^2+1/2mv_2^()'^2=3/4(1/2mv^2)`
Substituting the value, we get
`((1+e)/(2))^2+((1-e)/(2))^2=3/4`
or `(1+e)^2+(1-e)^2=3`
or `2+2e^2=3`
or `e^2=1/2`
or `e=1/sqrt2`
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Knowledge Check

  • Choose the most appropriate option. A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. The kinetic energy at the balls after the collision is 3/4th of the original. What is the coefficient of restitution?

    A
    `1//sqrt(3)`
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    C
    `sqrt(2)`
    D
    `sqrt(3)`

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    A
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    C
    `1/(sqrt2)`
    D
    `1/(sqrt3)`

  • A ball of 4 kg mass moving with a speed of 3ms^(-1) has a head on elastic collision with a 6 kg mass initially at rest. The speeds of both the bodies after collision are respectively

    A
    `0.6 ms^(-1), 2.4 ms^(-1)`
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    D
    `-0.6 ms^(-1), -2.4 ms^(-1)`

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