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Question

# A mass m is moving at speed v perpendicular to a rod of length d and mass M=6 m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is Md212. Then the angular speed of the system just after the collision is :

A
2v/d
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B
2v/(3d)
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C
v/d
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D
3v/(2d)
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Solution

## The correct option is A 2v/dSince there is no torque on the system, angular momentum will be conserved.Li=mvd2Lf=Iω=(Md212+m(d2)2)ω=(6md212+m(d2)2)ω=3md24ωLi=Lf⇒mvd2=3md24ω⇒ω=2v3d

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