The two uniform discs rotate separately on parallel axles. The upper disc (radius a and momentum of inertia ${\mathrm{I}}_1$) is given an angular velocity ${\mathrm{\omega }}_0$ and the lower disc of (radius b and momentum of inertia ${\mathrm{I}}_2$) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is

• A

  $\frac{\left({\mathrm{I}}_1{\mathrm{\omega }}_0\right)}{[{\mathrm{I}}_1+({\displaystyle \frac{{\mathrm{a}}^2{\mathrm{I}}_2}{{\mathrm{b}}^2}}\left)\right]}$

• B

  $\frac{\left({\mathrm{I}}_2{\mathrm{\omega }}_0\right)}{[{\mathrm{I}}_2+({\displaystyle \frac{{\mathrm{a}}^2{\mathrm{I}}_1}{{\mathrm{b}}^2}}\left)\right]}$

• C

  $\frac{\left({\mathrm{I}}_1{\mathrm{\omega }}_0\right)}{[{\mathrm{I}}_1+({\displaystyle \frac{{\mathrm{b}}^2{\mathrm{I}}_2}{{\mathrm{a}}^2}}\left)\right]}$

• D

  $\frac{\left({\mathrm{I}}_2{\mathrm{\omega }}_0\right)}{[{\mathrm{I}}_2+({\displaystyle \frac{{\mathrm{b}}^2{\mathrm{I}}_1}{{\mathrm{a}}^2}}\left)\right]}$