Question

The average density of the earth

• A. Is directly proportional to $\textit{g}$
• B. Is inversely proportional to $g$
• C. Does not depend on $g$
• D. Is a complex function of $g$

Answer 1

Answer: (A)

$\text{Density} = \frac{\text{Mass of earth}}{\text{Volume of earth}}$
$\rho = \frac{\textit{M}}{\left(4 / 3\right) \pi \left(\textit{R}\right)^{3}} = \frac{3 \textit{M}}{4 \pi \left(\textit{R}\right)^{3}}$ ..........(i)
$g=\frac{\textit{GM}}{\textit{R}^{2}}$ ...........(ii)
$\therefore $ $\frac{\rho }{g}=\frac{3 \textit{M}}{4 \pi \textit{R}^{3}}\times \frac{\textit{R}^{2}}{\textit{GM}}=\frac{3}{4 \pi \textit{RG}}$ or $\rho =\frac{3}{4 \pi \textit{RG}}g$
$\therefore $ The average density is directly proportional to $g$ .