Acceleration Due to Gravity

From Newton’s second law of motion, a force F exerted on an object produces an acceleration a in the object according to the relation:

F = ma

The force of gravity, i.e., the force exerted by the earth on a body lying on or near its surface, also produces an acceleration in the body. The acceleration produced by the force of gravity is called the acceleration due to gravity. It is denoted by the symbol g.

The magnitude of the force of gravity on a particle of mass m on the earth’s surface is given by:

F = GmM/R²

where M is the mass of the earth and R is its radius.

mg = GmM/R²

g = GM/R²

The force due to gravity on an object is directed towards the center of the earth. On the surface of the earth, the value of g is taken as 9.8 ms^–2.

The acceleration due to gravity produced in a body is independent of its mass. This means that a heavy ball and a light ball will fall with the same velocity.

Under the influence of gravity, a body falls vertically downwards towards the earth. For small heights above the surface of the earth, the acceleration due to gravity does not change much. Therefore, the equations of motion for initial and final velocities and the distance covered in time t are given by:

v = u + gt

s = ut + ½gt²

v² = u² + 2gs

A body falling with an acceleration equal to g is said to be in free-fall.