Answer: (4)
The average density of the earth = Mass/Volume
Mass of the earth = 5.97×1024 kg
The radius of the earth r = 6.37×106 m.
Even though the earth is not exactly a sphere but it is close enough.
Equation for the volume of the sphere
\(\begin{array}{l}V = \frac{4}{3}\times \pi \times r^{3}\end{array} \)
Let us consider
\(\begin{array}{l}g = \frac{GM}{R^{2}}\end{array} \)
\(\begin{array}{l}g = \frac{G \rho\times V}{R^{2}}\end{array} \)
\(\begin{array}{l}g = \frac{G \rho\times \frac{4}{3}\pi R^{2}}{R^{2}}\end{array} \)
\(\begin{array}{l}g = \frac{4}{3} \rho \pi G\end{array} \)
∴ g is directly proportional to average density.
