At time \( t = 0 \), a disk of radius \( 1 \, \text{m} \) starts to roll without slipping on a horizontal plane with an angular acceleration of \( \alpha = \dfrac{2}{3} \, \text{rad s}^{-2} \). A small stone is stuck to the disk. At \( t = 0 \), it is at the contact point of the disk and the plane. Later, at time \( t = \sqrt{\pi} \, \text{s} \), the stone detaches itself and flies off tangentially from the disk. The maximum height (in \( \text{m} \)) reached by the stone measured from the plane is \( \dfrac{1}{2} + \dfrac{x}{10} \). The value of \( x \) is ________. [Take \( g = 10 \, \text{m s}^{-2} \)]
