Explanation

(c) The value of acceleration due to gravity at a height $h$ above the earth’s surface is given by
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$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g^{''} = \frac{g}{\left( 1 + \frac{h}{R} \right)^{2}}$
where $R$ is radius of earth.
$When\ \ \ \ \ \ \ \ \ \ \ \ \ h = \frac{R}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g^{''} = \frac{g}{\left( 1 + \frac{h}{R} \right)^{2}} = \frac{4g}{9}$
$Hence,\ weight\ w^{''} = mg^{''} = \frac{4}{9}mg = \frac{4}{9}w.$