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For small distances compared with the Earth's radius, the decrease in acceleration due to gravity at a height h above the Earth's surface is equal to the decrease in g at a depth d below the surface. Which relation between d and h is correct?

1. d = 3h/2
2. d = h/2
3. d = h
4. d = 2h

Correct answer: d = 2h

Solution

For small h, g_h ~ g(1-2h/R) so decrease = 2gh/R; for depth, g_d = g(1-d/R) so decrease = gd/R. Equating: 2gh/R = gd/R gives d = 2h.

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