Assuming the Earth to be a sphere of uniform mass density, how much would a body weight half way down to the centre of the Earth, if it weighed `300N` on the surface of Earth.

Explanation

Let `m` be the mass of the body. The weight of body on the surface of Earth,
`W = mg = 300 N`.
When body is taken half down to the centre o fthe Earth, the depth of body, `d = R//2`
Acceleration due to gravity at depth `d` is,
`g' = g (1 - (d)/(R ))`
Weight of body at depth `d` is,
`W' = mg' (1 - (d)/(R )) = 300 (1 - (R//2)/(R ))`
`= 150 N`