Question

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

Answer 1

Weight of a body of mass $m$ at the Earth's surface,$W=mg=250N$

Body of mass $m$ is located at depth, $d=R_e/2$

Acceleration due to gravity at depth $g\left(d\right)$ is given by the relation:

$g^{\prime }=(1-\frac{d}{R_e})g$

$g^{\prime }=(1-\frac{R_e}{2R_e})g$

$=g/2$
Weight of the body at depth $d$,

$W^{\prime }=m{g}^{\prime }$

$=mg/2=W/2$

$=125N$