A body weighed 250 ~N on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh half way down to the centre of the earth?

Step-by-step solution

At a depth d below the surface of the earth, aligned & m g^ =G M^ m (R-d)^2 & M^ = 4 3 (R-d)^3 aligned aligned g^ & = G M^ (R-d)^2 & = 4 3 G (R-d) aligned If d= R 2 then g^ = 4 3 G = 2 G R 3 On the surface of the earth aligned g & = G m R V = 4 3 G R g^ & = g 2 aligned The body weighed 250 ~N on the surface of the earth would weigh 1 2 250=125 ~N , half way down towards the centre of the earth.