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A uniform rod OA of mass M and length 2a...

A uniform rod OA of mass M and length 2a rests on a smooth table and is free to turn about a smooth pivot at its end O, in contact with it at a distance b from O is an inelastic particle of mass m, a horizontal blow of impulse p is given to rod at a distance x from O in a direction perpendicular to the rod. The resultant intantaneous angular velocity of the rod is

A

`(px)/((4Ma^(2))/(3) + mb^(2)`

B

`(px)/M`

C

`(px)/(ma^(2)+mb^(2))`

D

none of these

Text Solution

Verified by Experts

a) Angualr impulse,
`J = DeltaL=Ideltaomega = l(omega-0) = lomega`
Here, `px = lomega`
`therefore` `omega = (px)/l + (px)/(mb^(2)+(M(2a)^(2))/3) = (px)/((4Ma^(2))/3 + mb^(2))`
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