Question

Average density of the earth :

• A. does not depend on $g$
• B. is a complex function of $g$
• C. is directly proportional to $g$
• D. is inversely proportional to $g$

Answer 1

Answer: (C)

is directly proportional to $g$

Answer 2

$g=\frac{GM}{R^{2}}; M=\left(\frac{4}{3}\pi R^{3}\right)\rho$ $\therefore g=\frac{4G}{3} \frac{\pi R^{3}}{R^{2}}\,\rho$ $\Rightarrow g=\left(\frac{4G\pi R}{3}\right)\,\rho$ $\left(\rho=average\, density \right)$ $\Rightarrow g\,\propto\,\rho$ or $\rho\,\propto\,g$