A body weighs 63 N on the surface of the earth.

Question:

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

Solution:

Weight of the body, $W=63 \mathrm{~N}$

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

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

Where,

g = Acceleration due to gravity on the Earth’s surface

Re = Radius of the Earth

For $h=\frac{R_{e}}{2}$

$g^{\prime}=\frac{g}{\left(1+\frac{R_{e}}{2 \times R_{e}}\right)^{2}}=\frac{g}{\left(1+\frac{1}{2}\right)^{2}}=\frac{4}{9} g$

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

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

$=m \times \frac{4}{9} g=\frac{4}{9} \times m g$

$=\frac{4}{9} W$

$=\frac{4}{9} \times 63=28 \mathrm{~N}$

 

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