Sliding sphere wear shape Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after this sphere slides (pure sliding no rolling) for sometime and assuming that it wears as it slides, what should be the shape of sphere after sliding? The one shown in (a) or (b)? In short, I want to know whether the worn side of sphere will be a straight line or a curved one? What will happen if a sphere slides against a sphere?  Also, I will highly appreciate if someone can refer to some good papers / books about this.
Edit: Additional assumptions
Lets assume that hardness of both surfaces is the same. Also assume that material is removed but is not attached to any of the surfaces (no adhesive wear). The phenomenon under consideration is abrasive wear (but no accumulation of wear debris). If a lubricant is in circulation, it is easy to realize this kind of wear

 A: It depends.  Assuming the lower surface is much harder than the sphere then :
If the sphere does not rotate at all as it slides then the answer is (a).
If the sphere rotates, ie rocks to and fro, as well as sliding, then it is (b).
On the other hand, if the sphere is harder than the lower surface, or the two surfaces have comparable hardness, then I think it will be something in between, even if the sphere does not rotate.  
As tfb says, the real situation is complicated.  For example, abraded material will accumulate at the edges of the depression hollowed out of the lower surface.  What effect will that have?  Will it provide lubrication?  Or enhance the amount of abrasion at the edges?  Also, if abraded material from the harder surface gets embedded in the softer surface, this suggests to me that wear will gradually tend towards being equal on each surface.    
This is a situation in which doing an experiment is essential if the outcome is crucial - by which I mean, if you will be making a decision which it could be costly to get wrong, either in time delay or money or even reputation.  Don't rely on theory or speculation.  Test it.
A: Given the diagrams you present, I believe a straight wear(A) on the sphere is most likely.  If the hardness of the surface is less than that of the sphere, there should be no, or almost no, wear on the sphere.  
(b) Would primarily occur if your surface was curved, such as if it were U shaped or in the case of sphere on sphere wearing. As you move along the curved surface, the moving sphere will be worn away along its "sides" which come into contact with the curved surface.   
Hope this helps!
