JEE Advanced 2022 — Paper 1 — Question 23

At time $\mathrm{t}=0$, a disk of radius 1 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 $\mathrm{t}=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{ } \mathrm{s}$, 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 $\qquad$ [Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$.]