**What is Acceleration due to Gravity?**

The acceleration gained by a freely falling object due to

*gravitational force/gravity*is called**. Its SI unit is***acceleration due to gravity**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 isAnd 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 isBy comparing these two equations we get

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*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 6 m.*

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

*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.