Disc A has moment of inertia $I$ and angular velocity $\omega$. Disc B has moment of inertia $2I$ and is initially at rest. When disc B is brought in contact with disc A, they acquire a common angular velocity. The loss of kinetic energy during the above process is\\
(A) $\frac{I\omega^2}{2}$\\
(B) $\frac{I\omega^2}{3}$\\
(C) $\frac{I\omega^2}{4}$\\
(D) $\frac{I\omega^2}{6}$