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Sudha Sarita said:Dropped objects hit the ground same time. Objects which are of point size with respect to Earth are attracted towards ground due to force of gravitation. Force of gravitation is given by formula F = G\frac{m_1m_E}{R^2}. When an object of mass m_1 is dropped means it has zero initial velocity. It experiences an acceleration towards Earth which is given by a = \frac{F}{m_1}. Depending on the mass of every object there can be variation in acceleration towards Earth over a wide range. Assume that all objects are dropped from the same height then on the basis of equation h = ut + 1/2 (at^2), time can vary over a range. I have not considered force due to air resistance.
This is very confusing and contradictory.
First of all, for m<<M, where M is mass of the Earth, then "g" is a constant. That is what we use in intro General Physics.
However, if you want to deal with this in general by stating that "... there can be variation in acceleration towards Earth over a wide range ...", then you can no longer use "h = ut + 1/2 (at^2)", because that kinematical equation was derived under the condition that acceleration is a constant!
Zz.