For the same total mass which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body
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For the same total mass which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body

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 four rods forming a square of side 2a.