A uniform ball of mass M and radius a can roll without slipping on the rough outer surface of a fixed sphere of radius b and centre O. Initially the ball is at rest at the highest point of the sphere when it is slightly disturbed.
Find the speed of the centre G of the ball in terms of the variable θ, the angle between the line OG and the upward vertical.
[Assume planar motion.] Show that the ball will leave the sphere when cos θ = 10/17.