[UPSC CSE 2017] Rigid Body Dynamics (Q200, 15M)

A diatomic molecule can be considered to be made up of two masses m_1 and m_2 separated by a fixed distance r. Derive a formula for the distance of centre of mass, C, from mass m_1. Also show that the moment of inertia about an axis through C and perpendicular to r is \mu r^2, where \mu=\dfrac{m_1m_2}{m_1+m_2}.