Strain in a freely falling body I wanted to know if there would be any extension in a freely falling body due to gravity . I know that a rod tied to the ceiling at one end will show an extension $MgL/2AY$. But if the same rod is falling freely under gravity, I am not able to go about this problem. Will the extension remain the same as that of the tied to the ceiling problem or will it change and how? Is it possible that there will be no extension at all?
 A: This is an interesting (and illuminating) question. The question to ask is as to what causes the stress in a body. The idea is that if different parts of a solid body are subjected to such external forces that they have a tendency to accelerate at different rates then the internal forces of the solid body will activate themselves so as to try to keep the different parts of the solid body from flying away from each other with such different accelerations. Of course, no solid body is perfectly rigid and thus, even with the presence of such internal forces (i.e., stress), there would be some deformation of the solid body (i.e., strain). 
Now, in the presence of gravity, if a solid body is freely falling (i.e., there are no external forces on the body except for the forces of gravity), then the acceleration of a material point of the body due to external forces (i.e., gravity) is just the same as the value of the gravitational field at the location of that material point. Thus, if the gravitational field is uniform, then all the material points of the body will accelerate with the same acceleration simply under the influence of the external force of gravity and the internal forces wouldn't need to activate themselves at all. However, if the gravitational field is non-uniform, then different material points of the body will tend to accelerate with different accelerations and thus, there would be some non-zero stress in the body. 
In your example, thus, if you treat the gravitational field of the Earth as a nearly uniform gravitational field then there would be no stress in the rod while it's freely falling. However, if you take into account the non-uniformity in the gravitational field of the Earth (which would be necessary if your object is big enough in its spatial extension), then non-zero stress would be induced in the rod. 
