The discs are rotating about their axes, normal to the discs and...

M.J. of $\mathrm{D}_1$ is $\mathrm{I}_1=\frac{\mathrm{MR}^2}{2}=\frac{2(0.2)^2}{2}=0.04 \mathrm{~kg} \mathrm{~m}^2$ initial angular velocity of $D_1$ is $\omega_1=50 \mathrm{rad} \mathrm{S}^{-1}$ M.J of $\mathrm{D}_2$ is $\mathrm{I}_2=\frac{4 \times(0.1)^2}{2}=0.02 \mathrm{~kg} m_2$ initial angular velocity of $\mathrm{D}_2$ is $\omega_2=$ 200 and $\mathrm{S}^{-1}$. According to the law of conservation of angular moment \begin{gathered}L_1=L_2 \\ \therefore \mathrm{I}}_{1} \omega_1+ \mathrm{I}}_{2} \omega_2=\left(\mathrm{I}}_{1}+ \mathrm{I}}_{2}\right) \\ \Rightarrow \omega=\frac{l_1 w_1+l_2 w_2}{\mathrm{I}_1+1}\\ \therefore \omega=\frac{(0.04)^2 \times 50+(0.02)^2 \times 200}{0.04+0.02}\\ =\frac{2+4}{0.06}=100 \mathrm{rads}^{-1} \end{gathered}