Define the intensity of the gravitational field and write its equation,unit,and dimensional formula.

(N/A) The gravitational force between two bodies separated by a distance is explained through the concept of a gravitational field:
$(1)$ Every object with mass produces a gravitational field around it.
$(2)$ This field exerts a force on any other body placed within it.
Definition of Gravitational Field Intensity: The gravitational force exerted by a source body on a unit mass placed at a given point is called the intensity of the gravitational field $(\overrightarrow{I})$ at that point. It is also known as gravitational field strength.
Consider a body of mass $M$ at the origin $O$ and a test body of mass $m = 1 \text{ kg}$ placed at point $P$ with position vector $\vec{r}$.
The gravitational force on the body of mass $m$ is given by $\overrightarrow{F} = -\frac{GMm}{r^2} \hat{r}$.
If $m = 1 \text{ kg}$,then $\overrightarrow{F} = \overrightarrow{I}$. Therefore,the intensity of the gravitational field is:
$\overrightarrow{I} = -\frac{GM}{r^2} \hat{r}$
The negative sign indicates that the gravitational force is attractive,directed towards the source mass $M$ (opposite to the position vector $\vec{r}$).
The magnitude of the gravitational intensity is:
$I = \frac{GM}{r^2}$
Unit: $\text{N/kg}$ (or $\text{m/s}^2$).
Dimensional Formula: $[M^0 L^1 T^{-2}]$.
If a body of mass $m$ is placed at point $P$,the gravitational force exerted by the field on it is $\overrightarrow{F} = m\overrightarrow{I} = -\frac{GMm}{r^2} \hat{r}$.