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If Earth’s radius became 1% smaller while its mass stayed unchanged, what would happen to the acceleration due to gravity at the surface?

1. It would fall by 1%.
2. It would fall by 2%.
3. It would rise by 1%.
4. It would rise by 2%.

Correct answer: It would rise by 2%.

Solution

With g = GM/R^2 and M fixed, g varies as 1/R^2, so dg/g = -2*(dR/R). A 1% decrease in R (dR/R = -1%) gives dg/g = +2%, i.e. g rises by 2%.

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