Question

Which of the following is correct expression for acceleration due to gravity on surface of earth -
($d$ is the density of earth and $R$ is radius of earth)

• A. $g=\frac{4}{3}\pi Gd$
• B. $g=\frac{4}{3}\pi RGd$
• C. $g=\frac{4}{3}\frac{\pi dG}{R}$
• D. $g=\frac{4}{3}\frac{\pi dG}{R^2}$

Answer 1

The correct option is B $g=\frac{4}{3}\pi RGd$

Acceleration due to gravity on surface of earth is
$g=\frac{GM}{R^2}=\frac{G\frac{4}{3}\pi R^{3}d}{R^2}$
$\Rightarrow g=\frac{4}{3}\pi GRd$