Atlearner-
April 19, 2023

March 14, 2022

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*.

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

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

By 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

Here,

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

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.

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