# What is Acceleration due to Gravity?

The acceleration gained by a freely falling object due to gravitational force/gravity is called acceleration due to gravity. Its SI unit is m/s2 and CGS unit is cm/s2. Acceleration due to gravity is a vector quantity because it has both magnitude and direction.

It is represented by the letter g. The value of g (In the standard unit system or SI unit system) on the surface of the earth at sea level is 9.8 m/s2.

## Measurement of acceleration due to Gravity

According to Newton's second law of motion (From F = ma), if m is the mass of an object which is in acceleration g then the force acting on it is

$F=mg$

And we also know from Newton's law of gravitation that if two masses m and M are separated by a distance r, then the gravitational force acting between them is

$F=\frac{GMm}{r^{2}}$

By comparing these two equations we get

$mg=\frac{GMm}{r^{2}}$

$or\;g=\frac{GM}{r^{2}}$

In the case of any point on the surface of the earth r = R (The radius of the earth R = 6400km). Then the formula for g goes like this

$g=\frac{GM}{R^{2}}$

This is the relation between G and g

Here,

G  = The universal gravitational constant = 6.67×10 -11 Nm2/kg2.

M = Mass of a very large body like Earth = 5.98 × 10 24 kg.

R = The radius of the earth = 6.38×10 m.

So the value of acceleration due to gravity on the earth is

$g=\frac{(6.67\times 10^{-11}N.m^{2}/kg^{2})(5.98\times 10^{24}kg)}{6.38\times 10^{6}m}$

or g ≈ 9.8 m/s2

## Variations in Acceleration due to gravity (g)

Acceleration due to gravity is not a constant quantity. Its value changes for various reasons, e.g.

• As the earth is elliptical, the value of g varies in different parts of the earth's surface.

• The value of g varies at different heights from the surface of the earth.

• The value of g varies at different depths from the surface of the earth

• The value of g varies in different parts of the earth's surface due to the rotational motion of the earth.