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

Question

Dr. Abubacker · Accepted Answer

(c) $g = \frac{GM}{R^{2}};g^{'} = \frac{GM}{R^{'2}} = \frac{GM(100)^{2}}{(99)^{2}R^{2}}$
% increase in $g = \frac{(g^{'} - g) 	imes 100}{g}$
$= \left( \frac{g'}{g} - 1 ight) 	imes 100 = \left\lbrack \left( \frac{100}{99} ight)^{2} - 1 ightbrack 	imes 100$
$\left\lbrack \left( 1 + \frac{1}{99} ight)^{2} - 1 ightbrack 	imes 100 \approx 2\%$

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

Explanation

Reviewed by Dr. Abubacker

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