Question

Let $M$and $R$denote the mass and radius of earth, respectively. The ratio of $\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$G$}\right.$ at the earth's surface is $\dots \dots \dots$

Answer 1

Concept of gravitational force

Gravitation force acting on mass m due to earth is $F_g=\frac{GMm}{R^2}\to \left(1\right)$

By, Newton's law $F_g=mg\to \left(2\right)$

Given

Let $M$and $R$denote the mass and radius of the earth.

In comparing 1 and 2, $g=\frac{GM}{R^2}$

Hence the ratio is $\frac{g}{G}=\frac{M}{R^2}$