A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal table and is free to rotate about a frictionless vertical axis fixed at one end. In Scenario 1, a small lump of sticky clay of mass \(M\) moving perpendicularly to the rod with speed \(v_0\) strikes and sticks to the free end of the rod, resulting in a post-collision angular velocity \(\omega_1\). In Scenario 2, an identical lump of clay moving with the same speed \(v_0\) strikes and sticks to the rod at its midpoint, resulting in a post-collision angular velocity \(\omega_2\). What is the ratio \(\dfrac{\omega_1}{\omega_2}\)?