A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth?

Acceleration due to gravity at a depth d from surface of earth
${\mathrm{g}}^{\mathrm{\prime }}=\mathrm{g}\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$...(1)
Where g = acceleration due to gravity at earth’s surface Multiplying by mass ‘m’ on both sides
of (1)
$\begin{array}{l}{\mathrm{mg}}^{\mathrm{\prime }}=\mathrm{mg}\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)\left(\mathrm{d}=\frac{\mathrm{R}}{2}\right)\\ =200\left(1-\frac{\mathrm{R}}{2\mathrm{R}}\right)=\frac{200}{2}=100\mathrm{N}\end{array}$