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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 R
The 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(12hRe) can be used only when h<<Re.

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