A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX1 is

Mass per unit length of the wire =ρ Mass of L length, M=ρL and since the wire of length L is bent in a form of circular loop therefore 2πR=L⇒R=L2π Moment of inertia of loop about given axis =32MR2=32ρLL2π2=3ρL38π2