Rotational Motion

At time t=0, a disk of radius 1m starts to roll without slipping on a horizontal plane with an angular acceleration of α=‌

2

3

‌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=√πs, 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 ‌

1

2

+‌

x

10

. The value of x is____ , [Take .g=10ms−2]