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Suppose the Earth's radius contracts by 1 percent while its mass stays the same. How would the value of g at the Earth's surface change?

1. increase by 2%
2. increase by 0.5%
3. decrease by 0.5%
4. decrease by 2%

Correct answer: increase by 2%

Solution

Since g = G*M/R² with M constant, g is inversely proportional to R². The fractional change is dg/g = -2*(dR/R). A 1% decrease (dR/R = -0.01) gives dg/g = +0.02 = +2%.

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