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Question

# Two balls of masses m and 2m are attached to the ends of a light rod of length L. The rod rotates with an angular speed ω about an axis passing through the centre of mass of system and perpendicular to the place. Find the angular momentum of the system about the axis of rotation.

A
23mωL2
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B
13ω2Lm
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C
23ω2Lm
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D
13Lm
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Solution

## The correct option is A 23mωL2Location of CM,xCM=2m×0+m×L2m+m=L3The velocity of ball A w.r.t. the centre of mass C isvA=ωxCM=ωL3vB=ω(L−xCM)=2ωL3Thus, angular momentum of a system about C,L=2mvAxCM+mva(L−xCM)=2m×ωL3×L3+m×2ωL3×2L3=2mωL23.

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