Small sphere of mass m moves to the right at a constant velocity υ_i (Figure a). The mass impinges and adheres to the upper end of a stationary mass rod M and a length d which can rotate without friction around a vertical axis passing through its center at point C (Figure b).

(a) Calculate the angular velocity of the system (agglomerate) immediately after the impact.

(b) Determine the ratio of the mechanical energy lost during impact to the original. The inertia moment of the rod relative to its axis of rotation is given I = 1/12 Md²