If the radius of the Earth were to shrink by | vedclass

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(B) The acceleration due to gravity $g$ is given by $g = \frac{GM_e}{R_e^2}$.Since mass $M_e = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R

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$W/2$

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(B) The acceleration due to gravity $g$ is given by $g = \frac{GM_e}{R_e^2}$.Since mass $M_e = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R_e^3 ho$,we have $g = \frac{G}{R_e^2} (\frac{4}{3} \pi R_e^3 ho) = \frac{4}{3} \pi G R_e ho$.This shows that $g \propto R_e$ when density $ho$ is constant.If the radius becomes $R_e' = \frac{R_e}{2}$,the new acceleration due to gravity $g'$ will be $g' = \frac{4}{3} \pi G (\frac{R_e}{2}) ho = \frac{1}{2} g$.Since weight $W = mg$,the new weight $W'$ is $W' = m g' = m (\frac{g}{2}) = \frac{W}{2}$.

If the radius of the Earth were to shrink by half while its density remains constant,what would be the weight of an object on the surface of the Earth?

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