Question

The relation between g and G is______________

Answer 1

1. The acceleration experienced by a body under free fall due to the gravitational force of the massive body is known as acceleration due to gravity $\left(g\right)$.
2. A universal gravitational constant $\left(G\right)$ is defined as the force of attraction between two objects with unit mass separated by a unit distance at any part of this universe. The numerical value of $G$ is $6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2$ .

Relationship Between $G$ and $g$

The relationship between $G$ which is known as the universal gravitational constant and $g$ known as acceleration due to gravity is given below.

$g=\frac{G\mathrm{M}}{R^2}$

Where,

$g$ is the acceleration due to the gravity of any given body in ${\mathrm{ms}}^{-2}$.
$G$ is the universal gravitational constant in ${\mathrm{Nm}}^2/{\mathrm{kg}}^2$.
$R$ is the radius of the given body in $\mathrm{km}$.
$\mathrm{M}$ is the mass of the given body in $\mathrm{kg}$.

Hence, the relation between g and G is $g=\frac{GM}{R^2}$.