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Question

# The value of acceleration due to gravity at certain height h above the surface of the earth is g4 , where g is the value of acceleration due to gravity at the surface of the earth. The height h is (R is the radius of earth)

A
R
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B
2R
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C
3R
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D
4R
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Solution

## The correct option is A RThe acceleration due to gravity at a distance r from the surface of a planet is given by g=GMr2 At the surface, g=GMR2...(1) At a height h, gh=GM(R+h)2...(1)From equation (1) and (2), we have ⇒gh=g(RR+h)2 As, gh=g4 ⇒g4=g(RR+h)2 Taking square root, ⇒12=RR+h ⇒h=R Hence, option (a) is the correct answer. Key Concept:The acceleration due to gravity due to a planet or point mass =GMr2 Why this question? Caution: The result g′=g(1−2hRe) can be used only when h<<Re.

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