The value of g^{'} at depth d is given by, g^{'}=g \\left( 1-\\dfrac{d}{R} \\right) The value of g^{'} at a distance x form Earth's centre is g^{'}= g \\left( 1-\\dfrac{R-x}{R} \\right) = \\dfrac{gx}{R} But g = \\dfrac{GM}{R^2} \\Rightarrow g^{'}=\\dfrac{\\left(\\dfrac {GM}{R^2} \\right)}{R} x=\\dfrac {GMx}{R^3} Force on a particle of mass m is mg=\\dfrac {GMmx}{R^3}