Average density of the earth (1) Complex function of g (2) Does not depend on g (3) Inversely proportional to g (4) Directly proportional to g

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.

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