A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m 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 Md²/12. Then the angular speed of the system right after the collision is
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Question

A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m 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 Md²/12. Then the angular speed of the system right after the collision is

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G1 Physics · Accepted Answer

Initial angular momentum about the axle is mvd/2. Final I = Md²/12 + m(d/2)² with M=6m, giving I=3md²/4. Hence ω=(mvd/2)/(3md²/4)=2v/(3d). Hence B. Use I=∫r²dm. For a shifted parallel axis use I=I about CM+Md²; for a plane lamina use I about z-axis=Iₓ+Iᵧ..