Question
If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.
✓
Answer
$g=\frac{G M}{R^{2}}$
$M =$ constant $g<\frac{1}{ R ^{2}}$
$100 \frac{\Delta g}{g}=-2 \frac{\Delta R}{R} 100$
$\%$ change $=-2(-2)$
$\%$ change in $g =4 \%$
increase by $4 \%$
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