Free fall

We know that the earth attracts objects towards it. This is due to the gravitational force. Whenever objects fall towards the earth under this force alone, we say that the objects are in free fall. while falling, there is no change in the direction of motion of the objects. But due to the earth’s attraction, there will be a change in the magnitude of the velocity. Any change in velocity involves acceleration. Whenever an objects falls towards the earth, an acceleration is involved. This acceleration is due to to the earth’s gravitational force. Therefore, this acceleration is called the acceleration due to gravitational force of the earth (or acceleration due to gravity). It is denoted by g . This unit of g is the same as that of acceleration, that is, m s^-2.

From second law of motion that force is the product of mass and acceleration. let the mas of the stone is m. Acceleration involved in falling objects due to the gravitational force and is denoted by g. Therefore the magnitude of the gravitational force F will be equal to the product of mass and acceleration due to gravitational force.

That is, F = mg

We know that, F = G M × m/d²

So, mg = G M × m/d²

g = G M/d²

Where, M = mass of the earth

d = distance between the object and the earth

The distance d is equal to R, which is the radius of the earth

mg = G M × m/R²

g = G M/R²

The earth is not a sphere. As the radius of the earth increases from the poles to the equator, the value of g becomes greater at the poles than at the equator.