Question

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half of radius of the earth? [NEET 2020]

Moderate

Solution

Given, $w = m g = 72 N$ (on the surface of earth)
At height equal to half of radius of the earth. $(i.e. h = \frac{R}{2})$
Acceleration due to gravity,
$g^{'} = g {(\frac{R}{R + h})}^{2} = g {(\frac{R}{R + R / 2})}^{2} = g (\frac{4 R^{2}}{9 R^{2}})$
$\Rightarrow g^{'} = \frac{4}{9} g$
Gravitational force on body at height h,
$F = m g^{'} = \frac{4}{9} m g = \frac{4}{9} \times 72 = 32 N$
or $w^{'} = 32 N$

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