Question

The average density of the earth

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

Answer 1

Answer: (A)

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