Question

A body weighs $72\text{N}$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of earth?

• A. $30\text{N}$
• B. $24\text{N}$
• C. $48\text{N}$
• D. $32\text{N}$

Answer 1

The correct option is D $32\text{N}$

Mass $m=\frac{72}{10}=7.2\text{kg}$
Now at some height $h$, acceleration due to gravity is given by

$g^{\prime }=\frac{g}{(1+\frac{h}{R}{)}^2}$
Here $h=\frac{R}{2}$
$g^{\prime }=\frac{g}{(1+\frac{1}{2}{)}^2}$ $=\frac{4}{9}g=4.44{\text{m/s}}^2$

Now the force experienced by the object at half the radius of earth is
$F^{\prime }=m{g}^{\prime }=7.2\times 4.44\approx 32\text{N}$