A particle slides on the surface of a fixed smooth sphere starting from the topmost point. Find the angle rotated by the radius through the particle, when it leaves contact with the sphere.
The angle rotated by the radius through the particle, when it leaves contact with the sphere is 
Explanation
The particle moving portrays a centripetal force of 
and a force of
, now equating the forces we get the equation as 
Calculating the value of velocity we get the value as
Hence, the real height is
Change in potential energy due to height is
Now placing the kinetic and potential energy together we get the change in angle as
1