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Question

If two objects with one having more mass than the other are both dropped from a particular height ,which one will touch the ground first and why?

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Solution

The answer of this question depends on the conditions of the medium that we’re performing this experiment in.

In free space/vacuum, both the bodies will reach the ground at the same time. This is because the only acceleration present is earth’s gravity, which points downwards (or radially inwards towards the center of the earth, but you get the point).
The time needed to reach the surface is the same for both the bodies, irrespective of their masses/weights.

s=ut+1/2at^2

where s is the distance covered, u is the initial speed (which we consider zero) and a is the acceleration (which we take as g =−9.8 m/s2), and tt is the time needed.

The answer to this question changes if we drop the bodies through a medium(air/liquid). Then the equation of motion is not so trivial. One then needs to consider the viscosity of the medium, the aerodynamics of the body, the weight of the body, and stuff like that. Then one cannot say with an absolute certainty (without calculating the equations of motion) that the bodies will reach the surface at the same time


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