Question bank/JEE Advanced/Physics

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 $\alpha=\frac{2}{3} \mathrm{rads}^{-2}$. 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 $\frac{1}{2}+\frac{x}{10}$. What is the value of $x$? $\left[\right.$ Take $\left.g=10 m s^{-2}.\right]$

Source: JEEBench (IIT Delhi) / JEE Adv 2022 Paper 1