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

Weight of body on the surface of earth
`mg = (GM m)/(R^(2)) = 300 N`
At depth, `d = R//3`, the weight of the body is
`mg' = mg (1 - (d)/(R )) = 300 (1 - (R//3)/(R )) = 300 xx (2)/(3)`
`= 200 N`