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 ?
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 ?
- [AIIMS 2018]
Weight of the body, $W=63 N$
Acceleration due to gravity at height $h$ from the Earth's surface is given by the relation
$g^{\prime}=\frac{g}{\left(\frac{1+h}{R_{r}}\right)^{2}}$
For $h=\frac{R_{r}}{2}$
$g^{\prime}=\frac{g}{\left(1+\frac{R_{e}}{2 \times R_{e}}\right)^{2}}=\frac{g}{\left(1+\frac{1}{2}\right)^{2}}=\frac{4}{9} g$
Weight of a body of mass $m$ at height $h$ is given as:
$W^{\prime}=m g$
$=m \times \frac{4}{9} g=\frac{4}{9} \times m g$
$=\frac{4}{9} W$
$=\frac{4}{9} \times 63=28 \;N$
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