Question
Average density of the earth-
A.
Is a complex function of $$g$$
B.
does not depend on $$g$$
C.
is inversely proportional to $$g$$
D.
is directly proportional to $$g$$
Answer :
is directly proportional to $$g$$
Solution :
$$\eqalign{
& g = \frac{{GM}}{{{R^2}}} = \frac{{G\rho \times V}}{{{R^{^2}}}}\,\,\,\,\, \Rightarrow g = \frac{{G \times \rho \times \frac{4}{3}\pi {R^3}}}{{{R^2}}} \cr
& g = \frac{4}{3}\rho \pi G.R{\text{ where }}\rho \to {\text{ average density}} \cr} $$