If Earth's radius were reduced by 1% while its mass remained unchanged, what would be the effect on the gravitational acceleration at its surface?
Increase by approximately 2%
Surface gravitational acceleration:
\(g = \dfrac{GM}{R^2}\)
With M constant, g is inversely proportional to R². A small fractional change gives \(\dfrac{\Delta g}{g} \approx -2 \dfrac{\Delta R}{R}\).
If R decreases by 1% (\(\Delta R/R = -1\%\)), then \(\Delta g/g \approx +2\%\).
Hence, g increases by approximately 2%.
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