A hollow sphere is released from the top of an inclined plane of inclination θ. (a) What should be the minimum coefficient of friction between the sphere and the plane to prevent sliding? (b) Find the kinetic energy of the ball as it moves down a length l on the incline if the friction coefficient is half the value calculated in part (a).
Given:
A hollow sphere is released from a top of an inclined plane of inclination θ.
To prevent sliding, the body will make only perfect rolling. In this condition,
And torque about the center
Putting the value of f in first equation
B) for kinetic energy of the ball
As we know, ω=αt
Kinetic energy=
Substituting the value of α, t, I and s
Kinetic energy= 
1