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A uniform rod AB of length L and mass m ...


A uniform rod AB of length `L` and mass `m` is suspended freely at A and hangs vertically at rest when a particle of same mass `m` is fired horizontally with speed `v` to strike the rod at its mid point. If the particle is brought to rest after the impact, then the impulsive reaction at A is horizontal direction is

Text Solution

Verified by Experts

The correct Answer is:
`mv//4`
Let the impulse on ball be `J`
`- J = 0 - mv`
`J = mv`
Let impulse reaction at `A` be `J'` On rod, angular impulse about 'A'
`J xx (l)/(2)= I omega rArr J xx (l)/(2) =((1)/(3) Ml^(2)) omega`
`J = (2)/(3) m lomega`….(2)
From (1) and (2)
`mv = (2)/(3) ml omega` or `(3v)/(2) = l omega` ...(3)
Let final vel. of `COM` of rod after collision `= v_(2)`
on rod `J- J' = mv_(2) (v_(2) =(l)/(2) omega)`
`J -momega(l)/(2) = J'` or`mv -m xx (3v)/(4) = J' "from" (3)`
or `J' = (mv)/(4)`.
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