Question

A body weighs $63$N on the surface of the earth. What is the gravitational force (in N) on it due to the earth at a height equal to half the radius of the earth ?

Answer 1

Weight of the body,$W=63N$
Acceleration due to gravity at height $h$ from the Earths surface is given by the relation:

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

Substituting $h=R_e/2$,

$g^{\prime }=4g/9$

Weight of body of mass m at height h is given as:

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

$=4/9mg$

$=4/9\times 63=28N$