Q. 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 ?
Solution:
Acceleration due to gravity at a depth d from surface of earth
$g' =g\left(1- \frac{d}{R}\right) $ ...(1)
Where g = acceleration due to gravity at earth's surface
Multiplying by mass 'm' on both sides of (1)
$mg' =mg\left(1- \frac{d}{R}\right) \left(d = \frac{R}{2}\right)$
$ = 200\left(1-\frac{R}{2R}\right) = \frac{200}{2} = 100 N$
