Two discs of moments of inertia I₁ and I₂ about their respective axes, rotating with angular frequencies ${\mathrm{\omega }}_1$and ${\mathrm{\omega }}_2$  respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

• A

  $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_1+{\mathrm{I}}_2{\mathrm{\omega }}_2}{{\mathrm{I}}_1+{\mathrm{I}}_2}$

• B

  $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_2+{\mathrm{I}}_2{\mathrm{\omega }}_1}{{\mathrm{I}}_1+{\mathrm{I}}_2}$

• C

  $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_1+{\mathrm{I}}_2{\mathrm{\omega }}_2}{{\mathrm{I}}_1-{\mathrm{I}}_2}$

• D

  $\frac{{\mathrm{I}}_1{\mathrm{\omega }}_2+{\mathrm{I}}_2{\mathrm{\omega }}_1}{{\mathrm{I}}_1-{\mathrm{I}}_2}$