Two coaxial discs, having moments of inertia I_1 and I_1/2, are rotating with respective angular velocities ω_1 and (ω_1)/2, about their common axis.…

Two coaxial discs, having moments of inertia $\displaystyle I_1$ and $\displaystyle \frac{I_1}{2}$, are rotating with respective angular velocities $\displaystyle \omega_1$ and $\displaystyle \frac{\omega_1}{2}$, about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If $\displaystyle \mathrm{E}_f$ and $\displaystyle \mathrm{E}_i$ are the final and initial total energies, then $\displaystyle \left(\mathrm{E}_f-\mathrm{E}_i\right)$ is :