A wooden wedge of mass `10 m` has a smooth groove on its inclined surface. The groove is in shape of quarter of a circle of radius `R = 0.55 m`. The inclined face makes an angle `theta =cos^(-1)((sqrt(11))/(5))` with the horizontal A block 'A' of mass m is palced at the top of the groove and given a gentle push so as to slide along the groove. There is no friction between the wedge and the horizontal ground on which it has been placed. Neglect width of the groove.

(a) Find the magnitude of displacement of the wedge by the instant the block A reaches the bottom of the groove
(b) Find the velocity of a wedge at the instant the block A reaches the bottom of the groove.