Two Disks Are Mounted on Low-Friction Bearings on a Common $\omega$

Multiple Choice

Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia I and is spinning with angular velocity $\omega$ . The second disc has rotational inertia 2I and is spinning in the same direction as the first disc with angular velocity 2 $\omega$ as shown. The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of:

A) 5 $\omega$ /3
B)
C)
D) $\omega$
E) 3 $\omega$