Define acceleration due to gravity. Derive an expression for acceleration due to gravity in terms of mass of the earth (M) and universal gravitational constant (G).

The acceleration produced in the motion of a body falling under the force of gravity is called acceleration due to gravity. It is denoted by ‘g’

The force (F) of gravitational attraction on a body of mass m due to earth of mass M and radius R is given by

F = G {𝑚𝑀 \over 𝑅^2}   … (1)

We know from Newton’s second law of motion that the force is the product of mass and acceleration.

∴ F = ma

But the acceleration due to gravity is represented by the symbol g. Therefore, we can write

F = mg    … (2)

From the equation (1) and (2), we get

mg = G {𝑚𝑀 \over 𝑅^2}  or g = {𝐺𝑀 \over 𝑅^2}  … (3)

When body is at a distance ‘r‘ from centre of the earth then g = {𝐺𝑀 \over 𝑅^2}