System of Particles and Rotational Motion

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:

Amount of energy loss (in J) in the collision is:

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x=L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is . [figure]