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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2022Gravitation

Solution:

$ g =\frac{ GM }{ R ^2} $
$ M =\text { 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 $4 \%$