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A mass m is moving at speed v perpendicu...

A mass `m` is moving at speed `v` perpendicular to a rod of length `d` and mass `M= 6m` pivots around a frictionless axle running through its centre and stickes to the end of the rod. The moment of inertia od the rod about its centre is `Md^(2)//12`. Then the angular speed of the system right after the collision us -

A

`2v//d`

B

`2v//(3d)`

C

`v//d`

D

`3v//(2d)`

Text Solution

Verified by Experts

The correct Answer is:
B

From conservation of angular momentum
`J = I omega`
`(d)/(2) xx mv = [(Md^(2))/(12) +m((d)/(2))^(2)] omega`
`(mvd)/(2) = [(6md^(2))/(12) +(md^(2))/(4)] omega`
`(mvd)/(2) = (3md^(2) omega)/(4)`
`omega =(2v)/(3d)`.
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