The uniform acceleration produced in a freely falling object due to the gravitational pull of the earth is known as acceleration due to gravity. It is denoted by g and its unit is m/s²

It is a vector quantity and its direction is towards the centre of the earth. The value of g is independent of the mass of the object which is falling freely under gravity. The value of g changes slightly from place to place. The value of g is taken to be 9.8 m/s² for all practical purposes.

The value of acceleration due to gravity on the moon is about. One sixth of that on the earth and on the sun is about 27 times of that on the earth.

 Among the planets, the acceleration due to gravity is minimum on the mercury.

Relation between g and a is given by

g = Gm / R²

Where M = mass of the earth = 6.0 * 10²⁴ kg and R = radius of the earth = 6.38 * 10⁶ m.

Acceleration due to gravity at a height h above the surface of the earth is given by

G_h = Gm / (R+h)² = g (1 – 2h / R)

Factors Affecting Acceleration Due to Gravity

1. Shape of Earth Acceleration due to gravity g & infi ; 1 / R² Earth is elliptical in shape. Its diameter at poles is approximately 42 km less than its diameter at equator. Therefore, g is minimum at equator and maximum at poles.

1.  Rotation of Earth about Its Own Axis If ω is the angular velocity of rotation of earth about its own axis, then acceleration due to gravity at a place having latitude λ is given by

g’ = g – Rω² cos² λ

At poles λ = 90° and g’ = g

Therefore, there is no effect of rotation of earth about its own axis at poles.

At equator λ = 0° and g’ = g – Rω²

 The value of g is minimum at equator

If earth stapes its rotation about its own axis, then g will remain unchanged at poles but increases by Rω² at equator.

1. Effect of Altitude The value of g at height h from earth’s surface

g’ = g / (1 + h / R)²

Therefore g decreases with altitude.

1. Effect of Depth The value of gat depth h A from earth’s surface

g’ = g * (1 – h / R)

Therefore g decreases with depth from earth’s surface.

The value of g becomes zero at earth’s centre.