The force of gravity acting on a body having unit mass placed on or near the surface of the Earth is known as acceleration due to gravity.
Let the earth to be a sphere of radius R and uniform density ρ, then mass will be
Mass = Volume ×Density
If point mass m is situated on the earth surface, then r = R and the gravitational force on the earth surface on mass m is
Let the mass m experiences acceleration g, called the acceleration due to gravity, then according to Newton’s second law of motion
This gives the acceleration due to gravity on the surface of the earth.
Substituting the value of M = 6.4×10²⁴ kg and R = 6.4×10⁶ m, we get g = 9.8 m/s².