A circular disc of mass M and radius R is rotating about its axis...

${I}_{1}{\omega}_{1} + {I}_{2}{\omega}_{2} = \left({I}_{1} + {I}_{2}\right) \times {\omega}_{f}$

$\dfrac{{MR}^{2}}{2} \times \omega + 0\left(\dfrac{{MR}^{2}}{2} + \dfrac{{MR}^{2}}{8}\right)\dfrac{16}{25}$

${\omega}_{f} = \dfrac{4}{5}\omega$

Final $K . E$., ${K}_{f} = \dfrac{1}{2}\left(\dfrac{{MR}^{2}}{2} + \dfrac{{MR}^{2}}{8}\right)\dfrac{16}{25}{\omega}^{2}$

${K}_{f} = \dfrac{{MR}^{2}{\omega}^{2}}{5}$ ; ${K}_{i} = \dfrac{1}{2}\left(\dfrac{{MR}^{2}}{2}\right){\omega}^{2} = \dfrac{{MR}^{2}{\omega}^{2}}{4}$

Percentage loss in kinetic energy $$