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A solid hemisphere of radius b has its flat surface glued to a horizontal table. a second solid hemisphere of different radius a rests on top of the first one so that the curved surfaces are in contac
A solid hemisphere of radius b has its flat surface glued to a horizontal table. a second solid hemisphere of different radius a rests on top of the first one so that the curved surfaces are in contact. the surfaces of the hemispheres are rough (so no slipping occurs between them), and both hemispheres have uniform mass distributions. the two objects are in equilibrium when the top one is "upside down", i.e. with its flat surface parallel to the table but above the hemispheres' contact point. show that this equilibrium position is stable if a < 3b / 5
