A uniform solid disk of mass \(M\) and radius \(R\) rotates about a fixed, frictionless axle through its center with an initial angular speed \(\omega_0\). At time \(t = 0\), a magnetic brake is engaged, exerting a resistive torque on the disk of magnitude \(\tau = \gamma \sqrt{\omega}\), where \(\gamma\) is a positive constant and \(\omega\) is the instantaneous angular speed. Which of the following integral expressions correctly represents the total number of revolutions \(N\) the disk completes before coming to rest?