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A uniform rod of length l and mass M rot...

A uniform rod of length `l` and mass `M` rotating about a fixed vertical axis on a smooth horizontal table. It elastically strikes a particle placed at a distance `l//3` from its axis and stops. Mass of the particle is -
.

A

`3 M`

B

`(3M)/(4)`

C

`(3 M)/(2)`

D

`(4M)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
From conservation of angular momentum
`I omega = mv (l)/(3) rArr (Ml^(2))/(12) xx omega = mv (l)/(m)`
`v = (Ml omega)/(4 m)` ….(1)
From conservation of `K.E`
`(1)/(2) I omega^(2) = (1)/(2) mv^(2)` ….(2)
from (1) & (2)
`(1)/(2) (Ml^(2))/(12) xx omega^(2) = (1)/(2) m xx ((Ml omega)/(4m))^(2) rArr m = (3)/(4) M`.
.
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