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21 November, 04:03

69) Half-way to the center of a planet of uniform density, your weight compared to that at the surface would be :

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  1. 21 November, 04:33
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    One - half

    Step-by-step explanation:

    Since the density is uniform

    Mass of the sphere = [ (4/3) π r^3] d

    where d is the uniform density.

    Mass of the sphere = [ (4/3) π d] r^3 = k r^3

    where k = [ (4/3) π d] is a constant

    Weight = mg = G m M / r^2 = G m [k r^3] / r^2 = G m k r

    Using Gauss' law for gravitation,

    Half way to the center of a planet the weight is only due to the inner sphere and the outer sphere does not contribute to his weight,

    Inside his weight is mg' = (G m k r) / 2 = mg/2

    Answer is one-half.
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