The acceleration due to gravity at height h above the Earth, for h ≪ R (where R is the radius of Earth), is given by:
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Question

The acceleration due to gravity at height h above the Earth, for h ≪ R (where R is the radius of Earth), is given by:

G1 Physics · Accepted Answer

At height h above Earth's surface, g' = GM/(R+h)² Since g = GM/R², we get g' = g/[1 + h/R]² For h ≪ R, use the binomial approximation: (1 + x)⁻² ≈ 1 − 2x Therefore, g' ≈ g(1 − 2h/R) Hence option D follows.