At time $t=0$, a disk of radius $1 \mathrm{~m}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} \mathrm{rad} \,\mathrm{s}^{-2}$. 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 $t=\sqrt{\pi} \,s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is $\underline{\hspace{2cm}}$ , [Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$.]