If the mass of the Earth decreases by 25 % an | vedclass

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(B) We know that the acceleration due to gravity is given by $g = \frac{GM}{R^2}$.Given that the mass of the Earth decreases by $25 \%$,the new mass $

Vedclass · Accepted Answer

$67$

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(B) We know that the acceleration due to gravity is given by $g = \frac{GM}{R^2}$.Given that the mass of the Earth decreases by $25 \%$,the new mass $M' = M - 0.25M = 0.75M = \frac{3}{4}M$.The radius of the Earth increases by $50 \%$,so the new radius $R' = R + 0.50R = 1.5R = \frac{3}{2}R$.The new acceleration due to gravity $g'$ is:$g' = \frac{GM'}{(R')^2} = \frac{G(0.75M)}{(1.5R)^2} = \frac{0.75GM}{2.25R^2} = \frac{0.75}{2.25} g = \frac{1}{3} g \approx 0.333g$.The decrease in acceleration due to gravity is $\Delta g = g - g' = g - 0.333g = 0.667g$.Expressed as a percentage,the decrease is $0.667 	imes 100 \% \approx 67 \%$.Therefore,the acceleration due to gravity at its surface decreases by nearly $67 \%$.

If the mass of the Earth decreases by $25 \%$ and its radius increases by $50 \%$,then the acceleration due to gravity at its surface decreases by nearly ......... $\%$

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