Why does a heavy and a light object falls at the same time?

When I first heard that a heavy and light object reaches the ground after the same time, I got baffled. But, to make up for this 'weird.' observation, I thought that, "The force of gravity is independent of the mass of the object." That was incorrect. I first realized the error in my thought when I discovered newton's famous equation:

        F = ma

I got confused as if someone has stung me in my mind. But after some research, I got the answer. That is what I am going to explain to you today. So read carefully. 

Lets again bring into consideration newton's equation that is 

        F = ma

 

The very first impression one would draw after seeing is that "Force is directly proportional to mass." Correct. But what if I changed the equation like this:

m = F/A

From this equation, it is clear that mass is indirectly proportional to acceleration.

In other words, it means that:

"The more we increase the mass of a substance, the more difficult it is to produce an acceleration." 

For example -  Suppose we have an object of mass 10 kg, if we want to provide it an acceleration of 5m/s square, then we have to apply a force of:

           F = 10 * 5

        = F = 50 Newton

But if we increase the mass of the object by 10 kg. Then, to provide the same acceleration, we have to apply a greater force. 

       F = 20 * 5

    = F = 100 Newton

This example proves that "The more we increase the mass of a substance, the more difficult it is to produce an acceleration." This property of the substance is called inertia, which is as we have proved, is proportional to the mass of the object.

Haven't we got our answer? Yes! Yes! Yes!

A heavy and light object reaches the ground at the same time as:

Although more force is applied to a heavy body, it possesses more inertia. 

Scientists have proven that these two things cancel out each other exactly, and so the resultant acceleration is equal for a light and a heavy body.

                                 

    THANKS FOR READING!

                                                                                                                              -Arvin Gupta