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
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
Decrease by $2\%$
Remain unchanged
Increase by $2\%$
Increase by $1\%$
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
$g = \frac{{GM}}{{{R^2}}}.$ If mass remains constant then $g \propto \frac{1}{{{R^2}}}$
$\%$ increase in $g = 2$($\%$ decrease in $R$) $=2 × 1\% = 2\%$.
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