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 XX' is

Question

G1 Physics · Accepted Answer

Loop radius R=L/(2π) and mass M=ρL. About a tangent-like in-plane axis XX′ use the parallel/perpendicular-axis geometry shown; substitution gives 3ρL³/(8π²). Hence D.