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Two particles of mases m and m' moving o...

Two particles of mases `m` and `m'` moving on parallel straight lines are at the distance `'a'` apart with velocities `v` and `v'(v gt v')`. The particles are connected by a string of length `( gt a)` which was loose in the beginning. Calculate the impluse of tension of the string when it becomes taut.

Text Solution

Verified by Experts

The correct Answer is:
`(m m'(v-v')sqrt(l^(2)-a^(2)))/((m+m')l)`

Just before string becomes taut

Just after string becomes taut.
`T Delta t = m(V cos theta-V'') , T Delta t = m'(V''-V' cos theta)`
`rArr v'' = ((m v+m'v') cos theta)/((m+m'))`
`T Delta t = J = (m m'(V-V')sqrt(l^(2)-a^(2)))/((m+m')l)`
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Knowledge Check

  • Two particles of mass m and 2 m moving in opposite directions collide elastically with velocities v and 2v. Find their velocities after collision.

    A
    0, 3v
    B
    1, 3v
    C
    0, 1v
    D
    0, 4v

  • Force acting on a particle of mass m moving in straight line varies with the velocity of the particle as F=K//V K is constant then speed of the particle in time t

    A
    `sqrt((kt)/(m))`
    B
    `sqrt((2kt)/(m))`
    C
    `2sqrt((kt)/(m))`
    D
    none of these

  • A mass m is hanging by a string of length l. The velocity v_(0) which must be imparted to it to just reach the top is

    A
    `sqrt3gl`
    B
    `sqrt4gl`
    C
    `sqrt5gl`
    D
    `sqrt6gl`