Acceleration due to gravity (g):

The acceleration created in a body, which is falling freely under the action of gravity of earth, is called acceleration due to gravity.

It is denoted by \( 'g' \).

The value of \( 'g' \) is \( 981cm/{sec}^2 \) in c.g.s. system. 32 \( ft/{sec}^2 \) in F.P.S. system and 9.8 \( m/{sec}^2 \) in S.I. system.

Let us consider the mass of the earth is \( M \) and the radius is \( R \). Let the acceleration due to gravity at a point \( P \) is \( g' \), which is at a distance \( r \) from the centre \( O \) of the earth. The height of the point \( P \) from the surface of the earth is \( h \). ( \( r=R+h \)).

Now, \( mg'=G\frac{Mm}{r^2} \\or,\ g'=\frac{GM}{r^2}=\frac{GM}{(R+h)^2} \),

where \( m \) is the mass of the body at the point \( P \) and \( G \) is the gravitational constant.

On the earth’s surface \( h=0 \), therefore \( r=R \).

So the acceleration due to gravity on the earth’s surface is,

\( g=\frac{GM}{r^2} \).