Question

If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would

• A. Decrease by 2%
• B. Remain unchanged
• C. Increase by 2%
• D. Increase by 1%

Answer 1

The correct option is C

Increase by 2%

$g=\frac{GM}{R^2}$. If mass remains constant then $g\propto \frac{1}{R^2}$
% increase in $g=2\left(\%decreaseinR\right)=2\times 1\%=2\%$