The moment of inertia of a straight wire about its perpendicular bisector and the moment of inertia of a circular frame about its perpendicular central axis are I₁ and I₂ respectively.

If the compositions of wires are same and lengths of the wires in them are equal, then:

For straight wire, I₁ = (ML²) / 12

For circular frame, I₂ = MR²

Since L = 2πR ⇒ R = L / (2π)

∴ I₂ = M(L²) / (4π²)

Hence, ratio:

I₁ / I₂ = (ML² / 12) / (ML² / 4π²) = π² / 3

Therefore, I₁ : I₂ = π² : 3