Total energy of ball at !!A!! and !!B!! are same if !!mu!! is:
- Very small, non zero
- Above a certain limit
Assume the ball is not deformed.
We need the energy at !!A!!,!!B!! to be same. So there should be no loss in energy. Energy can be lost only if the ball slips and there is friction.
So if there is no friction, then the energy of ball at !!A!! and !!B!! will be same.
If the ball rolls, even then the work done by friction will be zero. We are considering that the ball will not deform.
Now for the ball to roll, !!mu>(I/(MR^2)) (a/(gcos theta))!!.
Since the path is never vertical, so we can get a maximum value for !!mu!!.
Hence !!mu=0!! or it is greater than a particular limit