d
\(\,{(K.E.)_i} = \,\,\,\frac{1}{2}\,\,I{\omega ^2} + \frac{1}{2}\,\,m{v^2}\,\,\)

\( = \,\,\frac{1}{2}\,\, \times \,\,\frac{1}{2}\,\, \times \,\,2\,\, \times \,\,{(0.2)^2} \times \,\,{(3)^2} + \frac{1}{2}\,\, \times \,\,0.5\,\, \times \,\,{(5)^2}\,\,\)

\(= \,\,6.43\,\,J\)

\({(K.E.)_f}\, = \,\,\frac{1}{2}\,\,(I\,\, + \,\,m{R^2}){\omega ^2}\)

\( = \frac{1}{2}\,\,\left( {\frac{1}{2}\,\, \times \,\,2\,\,\, \times \,\,{{(0.2)}^2} + 0.5\,\,\,{{(0.2)}^2}} \right)\,\,\,{(10.3)^2}\,\, = \,\,3.18\,J\)

\( \Rightarrow \,\,\,{E_{loss}}\, = \,\,K{E_i} - K{E_f}\, = \,\,6.43\, - \,\,3.18\,\, \)

\(= \,\,3.25\,J\)