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