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 $G{\displaystyle \frac{m_1}{r^2}}$. The intensity of gravitational field at a point is given by equation $\overrightarrow{E}={\displaystyle \frac{\overrightarrow{F}}{m}}$, 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,
$\begin{array}{rl}& F\propto {\displaystyle \frac{m_1{m}_2}{r^2}}\\ & F=G{\displaystyle \frac{m_1{m}_2}{r^2}}\end{array}$
The term $G{\displaystyle \frac{m_1}{r^2}}$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-
$\overrightarrow{E}={\displaystyle \frac{\overrightarrow{F}}{m}}$
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 $\overrightarrow{F}=m\overrightarrow{g}$
$\begin{array}{rl}& \overrightarrow{E}={\displaystyle \frac{\overrightarrow{F}}{m}}\\ & \overrightarrow{E}={\displaystyle \frac{m\overrightarrow{g}}{m}}=\overrightarrow{g}\end{array}$
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.