Question

The density of earth in terms of acceleration due to gravity (g), radius of earth (R) and universal gravitational constant (G) is:

• A. $\frac{4\pi RG}{3g}$
• B. $\frac{3\pi RG}{4g}$
• C. $\frac{4G}{3\pi RG}$
• D. $\frac{3g}{4\pi R^{2}G}$

Answer 1

The correct option is D $\frac{3g}{4\pi R^{2}G}$

$g=\frac{GM}{R}g=G\rho \frac{4}{3}\frac{\pi R^3}{R}\rho =\frac{3g}{G4\pi R^2}\rho =\frac{3}{4}\frac{g}{\pi G{R}^2}$