Question Stem for Question Nos. 17 and 18

A uniform circular disk of radius $$0.2\,\mathrm{m}$$ and mass $$1\,\mathrm{kg}$$ is pivoted at its top point $$C$$ such that it can rotate freely around $$C$$ in the $$XY$$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass $$20\,\mathrm{g}$$, travelling along negative $$x$$ direction in the $$XY$$ 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 $$(g)=-10\hat{j}\,\mathrm{ms^{-2}}$$]

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