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

Explanation

`implies` Suppose, g and `g_d` are the acceleration due to gravity at the surface and at the depth d of earth respectively and `W and W_d` are the weights of body at the surface and at the depth of earth respectively.
`g(d) = g(1-d/R)`
`:. g(d) = g (1-(R/2)/R)" "[ :. d = R/2]`
`= g (1-1/2)`
`=g/2`
`:.`  Weight of body of mass m at depth d
W(d) = mg (d)
`=(mg)/2 " "[ :. g(d) =g/2]`
`W(d) = W/2 " "[ :. mg = W]`
`:. W(d) = (250)/2`
`:. W(d) = 125 N`