A uniform disc has radius R. If a concentric smaller disc of radius x is removed from the bigger disc then radius of gyration of the remaining disc about an axis passing through centre and perpendicular to plane of disc varies with x, according to the graph:-
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Question

A uniform disc has radius R. If a concentric smaller disc of radius x is removed from the bigger disc then radius of gyration of the remaining disc about an axis passing through centre and perpendicular to plane of disc varies with x, according to the graph:-

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G1 Physics · Accepted Answer

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. Substituting the geometry/mass distribution given in the question gives Image 3.