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Question

If the acceleration due to gravity at a height h from the surface of the earth is 96% less than its value on the surface, then h is (where R is radius of the earth).

A
.5R
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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 D 4Rthe gravitational acceleration at a height h above earth's surface is calculated as:gh=GM(R+h)2where, M is the mass of the earthR is the radius of the earth G is the universal Gravitational constantat the surface, g=GMR2Rearranging gh using the above equations as follows∴gh=GMR2×R2(R+h)2=g(RR+h)2In the given question, gh is 96% less than its value on the surface ⟹100−96=4% of its value on surface.∴gh=0.04g∴g(RR+h)2=0.04g∴RR+h=√0.04=0.2=15∴5R=R+h∴h=5R−R=4RThe gravitational acceleration is 96% less than its value on the surface of the earth at a height of 4R, where R is the radius of the earth.

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