Question

The gravitational field intensity due to earth is called acceleration due to gravity.
Explain.

Answer 1

Hint: Find the equation of acceleration due to gravity and gravitational field intensity. Acceleration due to gravity is g and equal to $G\dfrac{{{m}_{1}}}{{{r}^{2}}}$. The intensity of gravitational field at a point is given by equation $\overrightarrow{E}=\dfrac{\overrightarrow{F}}{m}$, Where $\overrightarrow{F}=m\overrightarrow{g}$.

Complete step by step answer:
Acceleration due to gravity-
The gravitational force between two masses is proportional to the product of mass and is inversely proportional to square of the distance apart,
$\begin{align}
  & F\propto \dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}} \\
 & F=G\dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}} \\
\end{align}$
The term $G\dfrac{{{m}_{1}}}{{{r}^{2}}}$is called acceleration due to gravity and is denoted by the letter g.
Gravitational field –
When a body is placed in a gravitational field, this field exerts a force on it. And the direction and the intensity of the field are defined in terms of the force it exerts on a body planed in it.
The intensity of gravitational field at a point is given by equation-
$\overrightarrow{E}=\dfrac{\overrightarrow{F}}{m}$
Where, $\overrightarrow{F}$= force exerted by the field on a body of mass m placed in a gravitational field.
If a mass m is placed close to the surface of the earth, the force on it is $\overrightarrow{F}=m\overrightarrow{g}$
$\begin{align}
  & \overrightarrow{E}=\dfrac{\overrightarrow{F}}{m} \\
 & \overrightarrow{E}=\dfrac{m\overrightarrow{g}}{m}=\overrightarrow{g} \\
\end{align}$
Thus the intensity of the gravitational field near the surface of the earth is equal to the acceleration due to gravity.

Note: When a body creates a gravitational field in a space around it. The field has its own existence and has energy and momentum. This field has a definite direction at each point of the space.
Acceleration due to gravity and intensity of the gravitational field are two separate physical quantities having equal magnitude and directions.