BdMO Online Forum

Is it possible to prove just by Thought Experiment (pure logic, no actual experiment) that a heavy object and a light object dropped from a certain height at a certain moment shall reach the ground at the same moment?
[Imagine a simple scenario: no air or other medium to resist the motion of the objects.]

I think so....
For any body of mass $m$ gravitational force acting on the body, $F=G\frac{M \times m}{R^2}$ (usual notations).
So, Acceleration of the body, $a=\frac{F}{m}=\frac{GM}{R^2}$, which is a constant.
$\therefore$ the acceleration of any freely falling body is constant.
If two bodies are at the same height $h$, time required by them to reach the ground, $t=\sqrt{\frac{2h}{a}}$.
This term contains only $h$ and $a$, both of which are constants, and no terms regarding $m$. So, under ideal conditions, i.e, in the absence of air, etc, any body, regardless of its mass, falling from the same height, will reach the ground at the same time.

You cannot arrive at any of the equations ($F=G\frac{Mm}{R^2}$, $a=\frac{F}{m}=\frac{GM}{R^2}$, $t=\sqrt{\frac{2h}{a}}$) just by logic and the information provided in the question. The equations are in fact the result of experiments, historically many years of various experiments and observations.

To further clarify the question,
You have only one premise given in the question:
1. Both a heavy object and a light object, when dropped from a height, fall to the ground after some time.

From this premise, you have only one of 3 possible conclusions to arrive at:
1. The heavy object reaches the ground earlier.
2. The light object reaches the ground earlier.
3. Both objects reach the ground at the same time.

You must use logic only. You cannot use any other established fact or observation if it does not logically follow the given premise.