Acceleration due to gravity

Acceleration due to gravity(g)
Acceleration due to gravity is defined as the acceleration produced in a freely falling body due to earth's gravity. It is denoted by 'g'. Its SI unit is m/s*2 and  its average value on the earth's surface is 9.8 m/s*2.
Relation between radius and acceleration due to gravity of earth
Let M be the mass of the earth with its radius R. If a body of mass m is on the surface of the earth.
According to the Newton's universal law of gravitation, we get
   F= GMm/R*2   ......(i)
Here F represents the force by which the body is attracted towards the earth. So, F represent the weight (W) of the object. ie.
  W=GMm/R*2    ......(ii)
We have, from the Newtons second law of motion,
   W= mg     ......(iii)
Hence from equation (ii) and (iii) we get,
    mg= GMm/R*2
       g = GM/R*2  ....(iv)
Equation (iv) is the expression for the acceleration due to gravity. This relation shows that, the value of g is,
i. directly proportional to yhe mass of the earth.
ii. inversely proportional to the square of radius of the earth.
iii. independent to the mass of the object lying on the earth's surface.

The value of g is different on didderent places of the earth because our earth is not a perdect sphere. The equatorial radius is greater than the polar radius. So, the value of g at poles is 9.83 m/s*2 and that in equatorial region is 9.78 m/s*2.

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