Question 52 - 2019 (10 Apr Shift 1)

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

(1) $-\frac{I_1\omega_1^2}{12}$

(2) $\frac{I_1\omega_1^2}{6}$

(3) $\frac{3}{8}I_1\omega_1^2$

(4) $-\frac{I_1\omega_1^2}{24}$