A uniform rod of linear mass density λ and length L is bent into a circular ring. The moment of inertia of the ring about any diameter is:
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Question

A uniform rod of linear mass density λ and length L is bent into a circular ring. The moment of inertia of the ring about any diameter is:

G1 Physics · Accepted Answer

The total mass of the rod is M = λL. After bending into a ring, L = 2πR ⇒ R = L/(2π). For a thin ring, moment of inertia about a diameter is I = ½MR². Substitute M = λL and R = L/(2π): I = ½(λL)[L²/(4π²)] = λL³/(8π²). Correct option: D.