Show that the moment of inertia for an axis perpendicular to the conjunction of a system of two bodies \(m_{1}, m_{2}\) spaced \(r\) apart and passing through C.M. is \(J=\mu r^{2}\), where \(\mu\) is the reduced mass of the system. Apply this to the \(\mathrm{CO}\) system (data given in question 3 ).

 Question 3

Determine the moment of inertia of a homogeneous circular corona, of surface density \(\sigma=1.25\) \(\mathrm{kg} \mathrm{m}^{-2}\), with inner radius \(r_{1}=0.30 \mathrm{~m}\) and outer radius \(r_{2}=0.50 \mathrm{~m}\).