a
Initial angular momentum of ring \( = I\omega  = M{R^2}\omega \)

If four object each of mass \(m\), and kept gently to the opposite ends of two perpendicular diameters of the ring then final angular momentum  \((M{R^2} + 4m{R^2})\omega '\)

By the conservation of angular momentumInitial angular momentum = Final angular momentum

\(M{R^2}\omega  = (M{R^2} + 4m{R^2})\omega '\) \(\omega ' = \left( {\frac{M}{{M + 4m}}} \right)\omega \)