Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds $\omega_1$ and $\omega_2$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis,the rotational $KE$ of the system will be:

• A
  $\frac{I_1\omega_1 + I_2\omega_2}{2(I_1 + I_2)}$
• B
  $\frac{(I_1 + I_2)(\omega_1 + \omega_2)^2}{2}$
• C
  $\frac{(I_1\omega_1 + I_2\omega_2)^2}{2(I_1 + I_2)}$
• D
  None of these