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Question

(A) The acceleration due to gravity $g$ on the surface of the earth is given by the formula: $g = \frac{GM}{R^2}$,where $M$ is the mass of the earth a

Vedclass · Accepted Answer

$3g / 4 \pi G R$

Vedclass · Answer

(A) The acceleration due to gravity $g$ on the surface of the earth is given by the formula: $g = \frac{GM}{R^2}$,where $M$ is the mass of the earth and $R$ is its radius.From this,we can express the mass $M$ as: $M = \frac{g R^2}{G}$.The density $D$ of the earth is defined as the mass per unit volume: $D = \frac{M}{V}$.Assuming the earth is a sphere,its volume $V$ is given by: $V = \frac{4}{3} \pi R^3$.Substituting the expressions for $M$ and $V$ into the density formula:$D = \frac{g R^2 / G}{4/3 \pi R^3} = \frac{g R^2}{G} 	imes \frac{3}{4 \pi R^3}$.Simplifying the expression,we get: $D = \frac{3g}{4 \pi G R}$.

Calculate the average density of the earth in terms of $g, G$ and $R$.

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