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Newton's Shell/Sphere Theorem

  1. Mar 17, 2013 #1

    h4d

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    1. The problem statement, all variables and given/known data

    A uniform solid sphere is inside and concentric with a spherical shell.

    M1=133kg ---mass of shell
    R1=2.42m ---radius of shell

    M2=278kg --mass of sphere
    R2=1.16m --radius of sphere

    a) Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 6 kg located at a distance 0.56 m from the center of the sphere and spherical shell.

    b) Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 6 kg located at a distance 1.66 m from the center of the sphere and
    spherical shell.

    c)Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 6 kg located at a distance 2.84 m from the center of the sphere and spherical shell.




    2. Relevant equations

    F=GMm/r^2

    3. The attempt at a solution
    For the first one, I thought that the answer should be zero because I believed that the force on point masses inside a sphere/shell was zero.

    I'm not sure how to begin with the rest because I think I'm overlooking something in the first part.
     
  2. jcsd
  3. Mar 17, 2013 #2

    ehild

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    Homework Helper
    Gold Member

    The gravitational force at distance r from a homogeneous sphere is the same as if all the mass contained in a sphere of radius r concentrated in the centre. So the gravitational force at 0.56 m from the centre is not zero.

    ehild
     
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