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Why do objects of different masses reach ground at same time ?

Before Galileo it was thought that heavy object weighs more.So it must fall down,since it has more weight (greater downward force applied to it). But that was proved wrong when Galileo threw two balls of different masses from Pisa tower.Where the 
heavier object get more mass that means it gets more inertia (more resistive to move).Hence,it needs more gravitational force (weight) to accelerate it at the same rate as the light one.

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