A particle of mass m is kept on a fixed, smooth sphere of radius R at a position, where the radius through the particle makes an angle of 300 with the vertical. The particle is released from this position. (a) What is the force exerted by the sphere on the particle just after the release? (b) Find the distance travelled by the particle before it leaves contact with the sphere.
The force exerted by the particle on the sphere is 
The distance travelled is 
Given
The mass of the particle is given as m, fixed on a sphere of radius R, where the particle makes a radius with an angle of 300 with vertical.
Formula Used
Using the conservation of static and dynamic energy such as potential and centripetal energy, we have the conservation equation as
where
m is the mass of the object, v is the velocity, R is the radius of the circular path, r is the radius of the object, h is the height.
Explanation
(a) The mass of the particle when horizontal is given as
Hence, force exerted by the sphere is
.
(b) The distance travelled by the particle in terms of radian/degree is calculated as
The change in potential energy due to the angle of 
is
Equating the kinetic and potential energy together we get the value of velocity as
And
The equation formed is
