If a body is taken up to a height of 1600km from the earth's surface, then the percentage loss of gravitational force acting on that body will be - (Radius of earth $R_{e}$ =6400 km).

50%

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36%

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25%

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10%

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Solution

The correct option is B 36%
$h = \frac{R_{e}}{4} g_{h} = \frac{g_{s}}{{(1 + \frac{h}{R_{e}})}^{2}} = \frac{g_{s}}{{(1 + \frac{1}{4})}^{2}} = g_{s} \frac{16}{25}$
So decrease in gravity $= g_{s} - g_{h} = \frac{9}{25} \times g_{s}$
$∴$ Percentage loss of gravitational force $= (\frac{9}{25} \times 100) % = 36 %$

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