The average density of the Earth:

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(A) The acceleration due to gravity $g$ at the surface of the Earth is given by $g = \frac{GM}{R^2}$.Substituting the mass $M = ho 	imes V = ho \

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is directly proportional to $g$

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(A) The acceleration due to gravity $g$ at the surface of the Earth is given by $g = \frac{GM}{R^2}$.Substituting the mass $M = ho 	imes V = ho 	imes \frac{4}{3}\pi R^3$,we get:$g = \frac{G 	imes ho 	imes \frac{4}{3}\pi R^3}{R^2} = \frac{4}{3}\pi G ho R$.From this expression,we can see that the average density $ho$ is given by $ho = \frac{3g}{4\pi GR}$.Since $G$,$\pi$,and $R$ (radius of the Earth) are constants,it follows that $ho \propto g$.Therefore,the average density of the Earth is directly proportional to $g$.

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