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There're two uniform hollow shells of radius $R$ and $2R$ each. The one with radius $R$ is inside the larger shell touching the larger shell's inner surface and its center. What's the net gravitational force on (i)surface of smaller sphere. (ii)region between smaller and larger sphere. (iii)surface of larger sphere.

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Anubhab Das
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    Can you clarify what you are asking? Are you asking about the net force between the two shells? If so this is a variant of the shell theorem. – John Rennie Jan 05 '16 at 08:22
  • Gravitational force on the outer shell due to the presence of inner shell – Anubhab Das Jan 05 '16 at 11:40
  • yes, but they're the same – Anubhab Das Jan 07 '16 at 12:06
  • Related: http://physics.stackexchange.com/q/150238/2451 and links therein. – Qmechanic Jan 07 '16 at 23:30
  • do you search for the field inside the outer shell or at its surface ? anyway, interesting results but trivial solution. In the question, replace why by what –  Jan 08 '16 at 03:20
  • @igael I did. Now please do answer. I'm just not getting this. – Anubhab Das Jan 12 '16 at 16:10
  • @AnubhabDas : ok. Are the spheres the same density ? Are the shells densities different than inside the spheres ? with the same density , it is equivalent to one sphere only , solvable by the shell theorem –  Jan 13 '16 at 07:05
  • They're of same density. Still, how to solve? – Anubhab Das Jan 13 '16 at 07:23
  • if they have the same density, you may ignore the 2nd sphere inside , it is just virtual ( in a gravity exercise ). Then apply the shell theorem with the 1st sphere. With different densities, you may start with the shell theorem for the 1st sphere and add the 2nd sphere with the difference of densities ( or reverse if the 2nd density if lower ) –  Jan 14 '16 at 07:34

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