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**Hint :**In this question, use the concept of the gravitational force and equate the force of attraction of the earth with the weight of a falling object. That will prove the required condition. The value of the the Newton's gravitational constant is $ G{\text{ }} = 6.67{\text{ }}x{\text{ }}{10^{ - 11}}{\text{N}}{{\text{m}}^{\text{2}}}{\text{/k}}{{\text{g}}^{\text{2}}} $ .

**Complete step by step answer**

Let us consider a body of mass $ m $ falling from a height $ h $ on earth’s surface.

Hence the weight of the body is $ mg $

Where, $ g $ is the acceleration due gravity of the earth.

Now we know that, if there are two objects of masses $ M $ and $ m $ respectively placed at a distance of $ r $ then the force acting between them will be-

$ \Rightarrow F = \dfrac{{GMm}}{{{r^2}}} $

Where, $ G $ is the Newton's gravitational constant, $ G{\text{ }} = 6.67{\text{ }}x{\text{ }}{10^{ - 11}}{\text{N}}{{\text{m}}^{\text{2}}}{\text{/k}}{{\text{g}}^{\text{2}}} $

So here in this case,

The force of attraction with which the earth attracts the falling object towards itself is,

$ \Rightarrow F = \dfrac{{GMm}}{{{{\left( {R + h} \right)}^2}}} $

Where, $ R $ is the radius of the earth and h is the distance above the earth’s surface from where the object is being thrown.

But, as we know $ R > > > > h $ , hence the above equation boils down to-

$ \Rightarrow F = \dfrac{{GMm}}{{{{\left( R \right)}^2}}} $

Now equating it with the weight of the object it becomes,

$ \Rightarrow \dfrac{{GMm}}{{{{\left( R \right)}^2}}} = mg $

Solving further we get,

$ \Rightarrow \dfrac{{GM}}{{{R^2}}} = g $

Which is the value of the acceleration due to gravity and from the above equation it is clear that $ g $ is independent from the mass of the falling object.

**Note**

Please note that the distance between the object’s surface is considered negligible, since the radius of the Earth is very large. If the same concept is applied to a large considerable distance, then the value of g will be a different quantity. Also, we can derive from the above activity that whether a soft feather is being thrown down to earth or a heavy metal ball is thrown, the acceleration due to gravity will be the same in both cases.

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