Question

Newton's 2nd law says that when a larger force is applied to an object of mass m, the object will experience a larger acceleration. At the same time, you've learned that all objects experience the same acceleration in a free fall, even if their weights (the forces of gravity acting on them) are different. That sounds like a contradiction: on one hand, from the Newton's 2nd law, a larger force means larger acceleration, on the other hand when applied to motion under gravity - a larger weight (force) means the same acceleration for all objects. How do you reconcile these statements? Why isn't it a contradiction? Does gravity violate the Newton's second law or is there another explanation. Be as thorough and clear in your explanation as possible.

Answer 1

There is no contradiction.

As stated by Galileo, two bodies of different masses, dropped from the same height, will reach the floor in same in the absence of air resistance.

Newton's gravitational force is proportional to the mass of a body, F=(GM×m)/R^2 , where M=mass of earth ,m=mass of object thrown F=GMR2×m, R is the radius of the earth, and G is Newton's gravitational constant.

Consequently, the acceleration of object is is a=F/m=(GM)/R^2 , which is independent of the mass of the object. Hence two objects that are subject only to the force of gravity will fall experience same acceleration and hence will reach the ground in the same time.

What I think you were missing is that the force F on the two bodies is not the same, but the accelerations are the same.Their masses are different and forces that is their weights are different but as seen above acceleration indepedent of mass .since  a=F/m=(GM)/R^2 everything is constant we have a constant acceleration,but since masses are different the force experienced by them that is their weights are different .