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Q.
Consider a body which weighs $w$ newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be
NTA AbhyasNTA Abhyas 2022
Solution:
The value of acceleration due to gravity at a height $h$ above the earth's surface is given by
$ \, g''=\frac{g}{\left(1 + \frac{h}{R}\right)^{2}}$
where $R$ is radius of earth.
When $h=\frac{R}{2}$
$g^{\prime \prime}=\frac{g}{1+\frac{h^2}{R}}=\frac{4 g}{9}$
Hence, weight $w^{\prime \prime}=m g^{\prime \prime}=\frac{4}{9} m g=\frac{4}{9} w$.
