Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D_1 has 2 kg mass and 0.2 m radius…

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $\displaystyle \mathrm{D}_1$ has $\displaystyle 2$ kg mass and $\displaystyle 0.2$ m radius and initial angular velocity of $\displaystyle 50 \mathrm{rad} \mathrm{s}^{-1}$. Disc $\displaystyle \mathrm{D}_2$ has $\displaystyle 4$ kg mass, $\displaystyle 0.1$ m radius and initial angular velocity of $\displaystyle 200 \mathrm{rad} \mathrm{s}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in $\displaystyle \mathrm{rad} . \mathrm{s}^{-1}$ ) of the system is :