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Q.

At what height above the surface of earth does the acceleration due to gravity become 36% of its value on the surface of earth if radius of earth is 6400 km?

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a

4267 km

b

3484 km

c

6824 km

d

1442 km

answer is B.

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Detailed Solution

$\frac{G M}{{(R + h)}^{2}} = \frac{36}{100} . \frac{G M}{R^{2}} \Rightarrow \frac{1}{R + h} = \frac{6}{10} \frac{1}{R} \Rightarrow h = \frac{2 R}{3}$

$∴ h = \frac{2 \times 6400}{3} k m = 4267 k m$

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