Question

The average density of the earth in terms of $g,G$and $R$ is:

• A. $\frac{4\pi GR}{3g}$
• B. $\frac{3g}{4\pi GR}$
• C. $\frac{3g}{4\pi G{R}^2}$
• D. $\frac{4\pi G{R}^2}{3g}$

Answer 1

Answer: (B)

$\frac{3g}{4\pi GR}$

The gravitational constant g is given as:
$g=\frac{GM}{R^2}orM=\frac{g\times R^2}{G}\Rightarrow DensityD=\frac{mass}{volume}=\frac{g\times R^2}{G\times V_e}$
(Where $V_e$ is the volume of the earth )
$D=\frac{g\times R^2}{G\times \frac{4}{3}\pi R^3}=\frac{3g}{4\pi GR}$.
Hence, the average density of the earth in terms of g, G and R is $\frac{3g}{4\pi GR}$.