A solid sphere of radius R and mass M slides without friction down a loop-the-loop track. The sphere starts from rest at a height of h above the horizontal. Assume that the radius of the sphere is small compared to the radius r of the loop.

(a) Find the minimum value of h in terms of r so that the sphere remains on the track all the way around the loop.
(b) Find the minimum value of h if, instead, the sphere rolls without slipping on the track.

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