Question

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

Answer 1

Step $1$:Given

Weight of the body $W=63N$

$h=$ Height$=R_e/2$

$R_e=$Radius of the earth
Step $2$:Acceleration due to gravity at height $h$

Acceleration due to gravity at height $h$ from the Earth's surface is given by the relation:

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

Substituting$h=\frac{R_e}{2}$,
$g\prime =\frac{4g}{9}$

Step $3$:Finding new weight

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

$$\begin{gathered} W\prime =mg\prime \\ =\frac{4}{9}mg \\ =\frac{4}{9}\times 63 \\ =28N \end{gathered}$$

The gravitational force on the body is 28 N.