Question

If the radius of the earth were to shrink by one per cent, its mass remaining the same, the value of $g$ on the earth's surface would

• A. increase by 0.5%
• B. increase by 2%
• C. decrease by 0.5%
• D. decrease by 2%

Answer 1

Answer: (B)

increase by 2%

Answer 2

$g = \frac{GM}{R^{2}} \Rightarrow \frac{dg}{g} = - 2 \frac{dR}{R}$
$\frac{dR}{R}= - 1 \% \Rightarrow \frac{dg}{g} =2 \%$