A uniform circular disk of radius \(0.2\,\text{m}\) and mass \(1\,\text{kg}\) 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 \(20\,\text{g}\), travelling along negative \(x\)-direction in the \(XY\)-plane with speed \(100\,\text{ms}^{-1}\), hits the circumference of the disk at a point \(P\). After collision the particle moves along negative \(y\)-direction at a speed of \(90\,\text{ms}^{-1}\). (Given: the acceleration due to gravity \(g = -10\hat{j}\,\text{ms}^{-2}\))
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:
