A particle of mass m slides from rest from position A, along a smooth circular track of radius R as shown in fig. (7a). The vertical distance travelled by m before leaving the surface of the track is

The speed y acquired by the particle after falling through a distance h (from A to B) is given by12mv2=mghThe contributed force needed at this instant ismv2R=m⋅2ghRor    v=2ghNow   mgcos⁡θ=mv2R¯or   R−h=2h∴    h=R/3