Official Answer Key & Detailed Solution
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Official UPSC Answer KeyUPSC Prelims 2003 • Science and Technology
Correct Answer: Option (B) — increase by 2%
Concept & Option Breakdown
Standard Reference VerifiedAcceleration due to gravity is $g = \frac{GM}{R^2}$. Taking fractional changes: $\frac{\Delta g}{g} \approx -2\frac{\Delta R}{R}$. If $R$ decreases by $1%$ ($\frac{\Delta R}{R} = -1%$), then $\frac{\Delta g}{g} = -2(-1%) = +2%$. Therefore, $g$ increases by approximately 2%.
Elimination Heuristic & Exam Approach
Use error formula: $\Delta g/g = -2(\Delta R/R)$. A $1%$ reduction in radius leads to a $+2%$ increase in $g$.
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