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The value of g at Earth’s surface is about 9.8 m/s^2. If Earth were of uniform density (same mass/volume throughout), what would the value of g be inside Earth at half its radius?

  • physics - ,

    g'(r) = G* m(r)/r^2, where m is the mass within radius r.
    G is the universal constant of gravity

    At r = R/2, 1/8 of the earth's total mass is inside. Call the value of g there g'.
    g'(at r = R/2) = G*(M/8)/(R/2)^2
    = (1/2)G*M/R^2

    = g/2 = 4.9 m/s^2

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