Question

The average density of the earth

• A. The complex function of g
• B. Does not depend on g
• C. Inversely proportional to g
• D. Directly proportional to g

Answer 1

The correct option is D

Directly proportional to g

Step 1: Given information

We know,

Mass of the earth $=5.97\times {10}^{24}\mathrm{kg}$

The radius of the earth $=6.37\times {10}^6\mathrm{m}$

The volume of a sphere,

$\mathrm{V}=\frac{4}{3}\times \mathrm{\pi }\times {\mathrm{r}}^3$

Step 2: To find

We have to determine the average density of the earth.

Step 3: Calculation

Let us consider,

$$\begin{gathered} \Rightarrow \mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2} \\ =\frac{\mathrm{G\rho }\times \mathrm{V}}{{\mathrm{R}}^2} \\ =\frac{\mathrm{G\rho }\times {\displaystyle \frac{4}{3}}{\mathrm{\pi R}}^2}{{\mathrm{R}}^2} \\ =\frac{4}{3}\mathrm{\rho \pi G} \end{gathered}$$

Therefore, the average density of the earth is directly proportional to g.