Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs 250 N on the surface of the earth.

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Solution

Given,

Weight= $m g = 250 N$
$g = \frac{G M}{r^{2}}$

$g^{'} = \frac{G M}{{(2 r)}^{2}} = \frac{1}{4} \frac{G M}{r^{2}} = \frac{g}{4}$

Weight become, = $m g^{'} = \frac{m g}{4} = \frac{250}{4} = 62.5 N$

Hence, weight at distance twice of earth radius is $62.5 N$

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Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs 250 N on the surface of the earth.

Given, Weight= mg=250N g=GMr2 g′=GM(2r)2=14GMr2=g4 Weight become, = mg′=mg4=2504=62.5N Hence, weight at distance twice of earth radius is 62.5N

Given,

Weight= $m g = 250 N$
$g = \frac{G M}{r^{2}}$

$g^{'} = \frac{G M}{{(2 r)}^{2}} = \frac{1}{4} \frac{G M}{r^{2}} = \frac{g}{4}$

Weight become, = $m g^{'} = \frac{m g}{4} = \frac{250}{4} = 62.5 N$

Hence, weight at distance twice of earth radius is $62.5 N$