AOB is a frictionless parabolic track in vertical plane. The equation of parabolic track can be expressed as `y = (3)/(2H) x^(2)` for co-ordinate system shown in the figure. The end B of the track lies at `y = (H)/(2)`. When a uniform small ring is released 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 D and it rolls without sliding. The ring leaves the track at F and attains a maximum height of `h_(2)` above the ground. Find the ratio `(h_(1))/(h_(2))`.

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

1.	AOB is a frictionless parabolic track in vertical plane. The equation of parabolic track can be expressed as `y = (3)/(2H) x^(2)` for co-ordinate system shown in the figure. The end B of the track lies at `y = (H)/(2)`. When a uniform small ring is released 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 D and it rolls without sliding. The ring leaves the track at F and attains a maximum height of `h_(2)` above the ground. Find the ratio `(h_(1))/(h_(2))`.
Answer» Correct Answer - `(h_(1))/(h_(2)) = (14)/(11)`

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