Angular Momentum & its Conservation question from JEE Main 2013 (25 Apr, Shift 1)

Answer: (c)

1. Loss when two bodies are coupled: $\Delta K = \frac{1}{2}\frac{I_1I_2}{I_1+I_2}\omega^2$ (second body initially at rest).
2. $I_1 = MR^2$ (ring), $I_2 = 2mR^2$ (two masses).
3. $\Delta K = \frac{1}{2}\cdot\frac{MR^2\cdot 2mR^2}{(M+2m)R^2}\omega^2 = \frac{Mm}{M+2m}\omega^2R^2$
4. So the answer is (c).