Question

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

Answer 1

One- half

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.