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Question

# The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface of earth for h << radius of earth

A

Is constant

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B

Increases linearly with h

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C

Increases parabolically with h

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D

Decreases

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Solution

## The correct option is B Increases linearly with h Let R be the radius of earth and g the acceleration due to gravity on earth's surface. Then the desired ration (say x) is : x=g(1−hR)g/(1+hR)2=(1−hR)(1+hR)2(1−hR)(1+2hR)2 (h<<R)≈1+hR From the expression we see that x increases linearly with h.

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