Rotational Motion

A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point $C$ such that it can rotate freely around $C$ in the $X Y$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g , travelling along negative $x$ direction in the $X Y$ plane with speed $100 \mathrm{~ms}^{-1}$, hits the circumference of the disk at a point $P$. After collision the particle moves along negative $y$ direction at a speed of $90 \mathrm{~ms}^{-1}$.

[Given : the acceleration due to gravity $(\mathrm{g})=-10 \hat{\jmath} \mathrm{~ms}^{-2}$ ]

After the collision the disk starts to rotate around point $C$ in the $X Y$ plane. The maximum change in the height (in m ) of its center $O$ is :