Two rigid hemispheres A and B with uniform volume density p have radii a and b, respectively. Hemisphere B has its flat face glued to a plane. Hemisphere A is then balanced on top of hemisphere B such that their curved surfaces are in contact.
Naturally, A is in equilibrium when its flat face lies parallel to the flat face of B. However, if given a small nudge, A rolls without slipping on the curved surface of B and will either oscillate about the equilibrium position or fall.
The constraint on aa such that A can oscillate is given to be kb>a, where k is some positive real number.
Find the value of k.
Assume that gravity points down, perpendicular to the plane of B's flat face.
(In reply to re: Thoughts on how to proceed - one error
by Kenny M)
Yes you are correct: we can't substitute a half circle. Must be a half sphere since the CG is different.
Edited on November 18, 2019, 2:47 pm
Posted by Larry
on 2019-11-18 14:46:26