A marble of mass m is placed on top of a bowling ball of radius r and allowed to roll from rest. derive the angle from centre of circle at which the marble loses contact with bowling ball. assume there is no friction between marble and bowling ball.

Answer 1

If there were no friction, the marble would slide, not roll. It is not clear which way they want this problem to be done.

In either case, a formula for the velocity of the marble vs. angle from the top can be derived. The rolling and sliding (no friction) cases will be different.

The marble will remain in contact with the bowling ball until
M g cos theta = M V^2/R
cos theta = V^2/(g R)

Knowing V(theta), you can solve for theta.

Answer 2

Although friction is needed to make the ball roll, it does not remove kinetic energy, because there is no "slipping" motion at the point of contact.