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 Balancing Hemispheres (Posted on 2019-11-15)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Thoughts on how to proceed - one error | Comment 4 of 9 |
(In reply to Thoughts on how to proceed by Kenny M)

Oops - fell into my own trap.  The c.g. of a solid hemisphere radius "r" is 3*r/8 up from the flat side, not 4*r/3/PI.

 Posted by Kenny M on 2019-11-18 12:21:57

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