[UPSC CSE 2023] Rigid Body Dynamics (Q181, 15M)

(i) Prove that the separation of two colliding particles is same, when observed in centre of mass and laboratory systems. (ii) Determine the kinetic energy of a thin disc of mass 0\cdot5\text{ kg} and radius 0\cdot2\text{ m} rotating with 100 rotations per second around the axis passing through its centre and perpendicular to its plane.