Slip, sliding away
A smooth sphere of radius r is glued to a table top. A small mass is resting at the exact top dead centre. It is given a very small disturbance and starts to slide over the surface of the sphere. How far below the top of the sphere does the object get before separating from the sphere?
Ignore the effects of rotation (the moment of inertia of the mass is negligible).
Neglect friction, buoyancy, air-resistance and all other such complications. This is not intended to be a trick (i.e. joke) problem.