A heavy flywheel rotates about a fixed axis. Due to fluid friction, the flywheel experiences an angular acceleration given by \(\alpha = -k \omega^{3/2}\), where \(k\) is a positive constant and \(\omega\) is its instantaneous angular velocity. At time \(t = 0\), the flywheel has an initial angular velocity \(\omega_0\). Which of the following expressions represents the time \(t\) required for the flywheel's angular velocity to decrease to \(\dfrac{\omega_0}{4}\)?