An object is sliding from top of a ball to the ground. This object starts from rest and slides without friction. At what height will the object get apart from the ball's surface if the radius of the ball is r meters?

Sorry to pick nits, but - an object that is at rest at the top of a sphere stays there.  This is the reverse of a pendulum which just has sufficient energy to be inverted.  The time the pendulum takes to reach the inverted position integrates up to infinity.

I have no doubt that what Charlie and Bractals calculated was what was intended.  In reality (if we can call frictionless sliding "reality" ;) ) the point of departure from the surface of the sphere would depend on the initial velocity of the object.  I think the intended result is the limit of the departure point as the initial velocity apporaches zero.

Posted by vswitchs on 2006-08-23 17:31:42