A circular disc of mass M and radius R is rotating about its axis with angular speed ω 1 . If another…

${\mathrm{I}}_1{\mathrm{\omega }}_1+{\mathrm{I}}_2{\mathrm{\omega }}_2=\left({\mathrm{I}}_1+{\mathrm{I}}_2\right)\times {\mathrm{\omega }}_{\mathrm{f}}$

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

${\mathrm{\omega }}_{\mathrm{f}}=\frac{4}{5}\mathrm{\omega }$

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

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

$$Percentage loss in kinetic energy $\%\mathrm{loss}=\frac{\frac{{\mathrm{MR}}^2{\mathrm{\omega }}^2}{4}-\frac{{\mathrm{MR}}^2{\mathrm{\omega }}^2}{5}}{\frac{{\mathrm{MR}}^2{\mathrm{\omega }}^2}{4}}\times 100=20\%$