A Wheel, with Rotational Inertia I, Mounted on a Vertical $\omega$

Multiple Choice

A wheel, with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed $\omega$ _0.A nonrotating wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown.The resultant combination of the two wheels and shaft will rotate at:

A) " $\omega$ ₀ /2"
B) "2 $\omega$ ₀"
C) " $\omega$ ₀ /3"
D) "3 $\omega$ ₀"
E) " $\omega$ ₀ /4"