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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, 1 Comments) Submitted on 2019-11-15 by Danish Ahmed Khan   
Difficulty: 3 of 5 Bonus: Tricky Ten Digit Number (in Numbers) Rating: 4.25
Find a number ABCDEFGHIJ, with all its digits different, such that:
  • A, C, E, G, and I are odd
  • HIJ is a multiple of BCD
  • GH is a multiple of AB
  • HIJ/BCD equals GH/AB
(No Solution Yet, 10 Comments) Submitted on 2006-07-31 by Yosippavar   
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