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Balancing Hemispheres (Posted on 2019-11-15) Difficulty: 5 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
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  Subject Author Date
SelfSantiago2020-05-06 22:10:12
GreatFrank2019-11-19 05:46:18
Here is a try ...Larry2019-11-18 14:47:38
re(2): Thoughts on how to proceed - one errorLarry2019-11-18 14:46:26
re(2): thoughts ...Larry2019-11-18 14:28:13
re: Thoughts on how to proceed - one errorKenny M2019-11-18 12:21:57
re: thoughts ...Kenny M2019-11-18 11:32:57
thoughts ...Larry2019-11-18 08:45:45
Thoughts on how to proceedKenny M2019-11-16 16:41:13
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