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Question
Why is acceleration due to gravity of earth independent of mass?
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Solution
F = GMm/r^2 where G is the gravitational constant, r is in this case the distance between the centre of the Earth and the object the gravitational force is acting on, and most importantly, M and m are the mass of the Earth and the mass of the object, respectively.
Of course, as well as this, F = mg
Thus, F = mg = GMm/r^2 and this can be rearranged to find g = GM/r^2
It can be observed from this that the mass of the object cancels out, so it is of no consequence to the acceleration it undergoes as a result of gravity.
F = GMm/r^2 where G is the gravitational constant, r is in this case the distance between the centre of the Earth and the object the gravitational force is acting on, and most importantly, M and m are the mass of the Earth and the mass of the object, respectively.
Of course, as well as this, F = mg
Thus, F = mg = GMm/r^2 and this can be rearranged to find g = GM/r^2
It can be observed from this that the mass of the object cancels out, so it is of no consequence to the acceleration it undergoes as a result of gravity.
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