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The first ball of mass m moving with a v...

The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, the ratio of final velocity of the second ball to the initial velocity of the first ball is 

A

`(1 - e)/(1 +e)`

B

`(1 + e)/(1 - e)`

C

`(1 + e)/(2)`

D

`(1 - e)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
According to conservation of linear momentum, we get
`m u + 0 = mv_1 + mv_2`
or `u = v_1 + v_2 " " ………(i)`
Coefficient of restitution, `e = (v_2 - v_1)/(u_1 - u_2) `
But `u_1 - u_2 = u " " ( :. u_2 = 0)`
`:. e = (v_2 - v_1)/(u)`
or `eu = v_2 - v_1 " " .....(ii)`
Addition equations (i) and (ii), we get
`u (e + 1) = 2 v_2 " or " v_2 = (u(e + 1))/(2)`
`:. ("Final velocity of " 2^(nd) "ball")/("Initial velocity of " 1^(st) " ball) = (v_2)/u = (e + 1)/(2)`.
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Knowledge Check

  • A ball of mass moving with a velocity u collides head on with a ball B of mass m at rest. If the coefficient of restitution is e. the ratio of final velocity of B to the initial velocity of A is

    A
    `(1-e)/(1+e)`
    B
    `(1+e)/(1-e)`
    C
    `(1+e)/2`
    D
    `(1-e)/2`

  • The first ball of mass m moving with the velocity upsilon collides head on with the second ball of mass m at rest. If the coefficient of restitution is e , then the ratio of the velocities of the first and the second ball after the collision is

    A
    `(1-e)/(1+e)`
    B
    `(1+e)/(1-e)`
    C
    `(1+e)/(2)`
    D
    `(1-e)/(2)`

  • A ball of mass m moving with velocity v collides head-on which the second ball of mass m at rest. I the coefficient of restitution is e and velocity of first ball after collision is v_(1) and velocity of second ball after collision is v_(2) then

    A
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    B
    `v_(1)=((1+e)u)/(2),v_(2)=((1-e)u)/(2)`
    C
    `v_(1)=u/2,v_(2)=-u/2`
    D
    `v_(1)=(1+e)u,v_(2)=(1-e)u`

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