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Question

The variation of acceleration due to gravity g with distance d from the center of the earth is best represented by (R= Earth’s radius):

A
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B
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C
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D
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Solution

The correct option is A
As we know that acceleration due to gravity on the surface of the earth is gs=GMR2
Acceleration due to gravity inside the earth (at depth d) : -
gs=GMR2 ... (1)
ρ=MV=M43πR3
M=ρ(43πR3)
From equation (1)
gs=GR2(ρ43πR3)
gs=43GρπR
at depth d:g=43πρG(Rd)
linear relation
Acceleration due to gravity above the surface of the earth:
gs=GMR2
at height h
g=GM(R+h)2
g=GMR2(1+hR)2
relation is parabola
The correct option is (A).

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