A rigid wheel with rotational inertia \(I = MR^2\) is mounted on a fixed, frictionless horizontal axle and consists of two concentric spools of radii \(R\) and \(2R\).

In Scenario 1, a light cord is wrapped around the inner spool of radius \(R\) and attached to a hanging block of mass \(M\).

In Scenario 2, the cord is instead wrapped around the outer spool of radius \(2R\) and attached to the same block of mass \(M\), leaving the inner spool empty.

If both systems are released from rest, what is the ratio of the vertical displacement of the block in Scenario 2 to that in Scenario 1 after an identical time interval \(\Delta t\)?