In this chapter, we will discuss the acceleration due to gravity on an object on the surface of the Earth.
Acceleration due to Gravity
Acceleration due to gravity is the acceleration produced in a freely falling body under the effect of the Earth's gravitational force only.
In the previous chapter, we termed the Earth's gravitational force on a comparatively smaller object as gravity. Also, Newton's second law gives us an equation for the quantitative definition of force. We generalize this equation as
\begin{equation} \rm F = m a \end{equation}
where the symbols have their usual meaning.
Let, M=mass of the earth, m=mass of the object, R=radius of the earth
According to the Newton's law of gravitation: $ \hspace {1cm}F=\frac{GMm}{r^2}\hspace {1cm} (i)$
According to the Newton's second law of motion: $ \hspace {1cm}F=mg\hspace {1cm} (ii)$
From (i) and (ii)
$\hspace {1cm}mg=\frac{GMm}{r^2}$
$\hspace {1cm}\therefore\hspace {1cm}g=\frac{GM}{r^2}$