Acceleration Due to Gravity

The speed of a falling stone increases continuously. The stone is accelerated due to force of attraction between the stone and the earth. This acceleration is called the acceleration due to gravity.

Two objects of different masses would reach the ground together when dropped from the same height. Acceleration due to gravity is same for any mass at a given place. The SI unit of g is same as that of acceleration - ms–2.

Force is product of mass and acceleration. Therefore, the magnitude of force of gravity 'F' is equal to product of mass and acceleration due to gravity.

F = mg

F = mg = GMm/r2

g = GM/r2

M is the mass of the earth and r is the distance between the object and the centre of the earth. If the object is on or near the surface of the earth, the distance r in equation will be equal to the radius of the earth R.

g = GM/R2

The value of g is independent of the mass of the freely falling body. The radius of the earth is not same at all the places on the surface of the earth. So the value of 'g' changes from place to place on the earth. Its value is greater at the poles than at the equator. The average value of ‘g’ on and near the surface of the earth is taken as 9.8 ms–2.

g = 9.8 ms-2

Variation in g

On the surface of earth the value of g is minimum at the equator. It increases on moving towards the poles and is maximum at the poles.

The value of g decreases on moving above or below the surface of earth. It is zero at the centre of the earth.