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The accelaration produced in the motion by a falling body under the influence of gravitational attraction of earth is called the accelaration due to gravity 
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Acceleration due to gravity is the ratio between the weight of a body and its mass.

   g = W / m

Acceleration due to gravity = acceleration in the vertically downward direction of a body which is freely falling from above the surface of Earth  towards the center of Earth.

Newtons' universal law of gravitation:  F  =  G M  m / R²

   where F = force of attraction on mass m due to Earth
                 M = mass of Earth
                 m = mass of a body on the surface of Earth
                 R = radius of Earth

   Gravitational force on a body on the surface of Earth is its weight.
         W =    F = m g = G M m / d²

     => g = G M / d²
               this is called the acceleration due to gravity on the surface of a planet.

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