Explain gravitational intensity.

(N/A) The force exerted mutually on two bodies separated by some distance is explained to occur through the field as follows:
$(1)$ Every object produces a gravitational field around it due to its mass.
$(2)$ This field exerts a force on another body lying in this field.
Intensity of gravitational field: The gravitational force exerted by a given body on a body of unit mass at a given point is called the intensity of gravitational field $(\overrightarrow{I})$ at that point. It is also known as gravitational field strength or gravitational intensity.
Suppose a body of mass $M$ is at the origin $O$ of a coordinate system and a body of mass $m = 1 \text{ kg}$ is placed at point $P$ having position vector $\vec{r}$.
The gravitational force on the body of mass $m$ due to $M$ is $\overrightarrow{F} = -\frac{GMm}{r^{2}} \hat{r}$.
If $m = 1 \text{ kg}$,then $\overrightarrow{F} = \overrightarrow{I}$ (intensity of gravitation),therefore:
$\overrightarrow{I} = -\frac{GM(1)}{r^{2}} \hat{r} \quad \ldots \ldots \ldots(1)$
Here,the force exerted by the body of mass $M$ on the body of mass $m$ is directed toward $O$,whereas the position vector and unit vector are directed from $O$ to $P$,hence the negative sign is present in the formula.
The magnitude of the intensity of gravitation is:
$I = \frac{GM}{r^{2}} \quad \ldots \ldots \ldots(2)$
Its $SI$ unit is $\text{N/kg}$ and its dimensional formula is $M^{0} L^{1} T^{-2}$.
If a body of mass $m$ is placed at this point $P$,the gravitational force exerted by the field on it is $\overrightarrow{F} = m\overrightarrow{I} = -\frac{GMm}{r^{2}} \hat{r}$.