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If the Earth were to shrink to 50% of its present radius while keeping the same mass, the weight of a body on its surface would
AIncrease by 50%
BIncrease by 300%
CDecrease by 50%
DDecrease by 25%
Answer & Solution
Correct answer: B. Increase by 300%
1. Weight W = mg and g = GM / R², so W is proportional to 1/R² for fixed mass M.
2. New radius R' = R/2, so new g' = GM / (R/2)² = 4 x GM / R² = 4g.
3. New weight is 4W, an increase of 4W − W = 3W, that is 300%.
4. Rule out +50%: that wrongly treats g as proportional to 1/R instead of 1/R².
_Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 1 "Laws of Motion", p.20_
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