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 ?

Question

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Answer 1

Weight of the body, $W = 63 N$
Acceleration due to gravity at height $h$ from the Earths surface is given by the relation:
$g^{'} = \frac{g}{( 1 + \frac{h}{R _{e}} ) ^{2}}$
Substituting $h = R_{e} / 2$ ,

$g^{'} = 4 g / 9$

Weight of body of mass m at height h is given as:
$W^{'} = m g^{'}$
$= 4 / 9 m g$
$= 4 / 9 \times 63 = 28 N$

Answer 2

Weight of the body,

W = 63 N

Acceleration due to gravity at height

h

from the Earths surface is given by the relation:

g^{'} = \frac{g}{( 1 + \frac{h}{R _{e}} ) ^{2}}

Substituting

h = R_{e} / 2

,

g^{'} = 4 g / 9

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

W^{'} = m g^{'}

= 4 / 9 m g

= 4 / 9 \times 63 = 28 N