AOB is a frictionless parabolic track in vertical plane. The equation of parabolic track can beexpressed as y = (3)/(2H) x^(2) for co-ordinate systemshown in the figure. The end B of the tracklies at y = (H)/(2). When a uniform small ring isreleased on the track at A it was found to attain a maximum height of h_(1), above the ground after leaving the track at B. There is another track DEF which is in form of an arc of a circle of radius H subtending an angle an angle of 150^(@) at the centre. The radius of the track at D is horizontal. The same ring is released on this track at point Dand it rolls without sliding. The ring leaves the track at F and attains a maximum height of h_(2)above the ground. Find theratio (h_(1))/(h_(2)).

AOB is a frictionless parabolic track in vertical plane. The equatio

1.	AOB is a frictionless parabolic track in vertical plane. The equation of parabolic track can beexpressed as y = (3)/(2H) x^(2) for co-ordinate systemshown in the figure. The end B of the tracklies at y = (H)/(2). When a uniform small ring isreleased on the track at A it was found to attain a maximum height of h_(1), above the ground after leaving the track at B. There is another track DEF which is in form of an arc of a circle of radius H subtending an angle an angle of 150^(@) at the centre. The radius of the track at D is horizontal. The same ring is released on this track at point Dand it rolls without sliding. The ring leaves the track at F and attains a maximum height of h_(2)above the ground. Find theratio (h_(1))/(h_(2)).
Answer» ANSWER :`(h_(1))/(h_(2)) = (14)/(11)`