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The moment of Inertia of such a system would be (3/2)MR2 .
The moment of Inertia of the system = The moment of Inertia of Ring rotating about an axis perpendicular to its plane + The moment of Inertia of Ring rotating about an axis in its own plane.
The moment of Inertia of Ring rotating about an axis perpendicular to its plane= MR2
The moment of Inertia of Ring rotating about an axis in its own plane.= MR2/2
So the moment of inertia of the system is (3/2)MR2
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