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How far below the Earth's surface (Earth radius R) must a person descend so that their weight becomes one-fourth of its value at the surface?

1. R/4
2. R/2
3. 3R/4
4. None

Correct answer: 3R/4

Solution

Assuming uniform density, the acceleration due to gravity at depth d is g_d = g(1 - d/R). For the weight to be one-fourth: g(1 - d/R) = g/4 -> 1 - d/R = 1/4 -> d/R = 3/4 -> d = 3R/4.

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