A horizontal, uniform disk of mass \(M\) and radius \(R\) rotates freely about a vertical axle through its center with an initial angular velocity \(\omega_0\). Friction in the axle is negligible. A small block, also of mass \(M\), is dropped from a negligible height onto the disk and sticks to it. Two scenarios are considered:

Scenario 1: The block is dropped onto the disk at a distance \(r = \dfrac{R}{2}\) from the axle.
Scenario 2: The block is dropped onto the disk at the rim, at a distance \(r = R\) from the axle.

If \(\omega_1\) is the final angular velocity of the system in Scenario 1 and \(\omega_2\) is the final angular velocity in Scenario 2, what is the ratio \(\dfrac{\omega_1}{\omega_2}\)?