Collision between two non-deformable objects Let say we have a non-deformable object and we release it into free fall and it hits the non-deformable floor. What would happen?
Here is the way I think. 
Since the floor and the object are both non-deformable, there is no chance that the object will bounce. If we assume the Earth to be at rest before and after the collision (*), the object stops suddenly (like in 0,0000000000.. second) and that means the acceleration and the force are infinitely big. 
This reasoning makes me think that there are no such things as perfect non-deformable bodies but let say we use the closest object and the floor to conduct the experiment. What would happen both in terms of momentum and energy conservation?
*In reality the Earth would be moving towards the object during free fall so that the center of mass of the system stays unchanged.
 A: Collisions between non-deformable objects violate Newton's laws. By Newton's second law and third laws, we have $a_1/a_2=m_2/m_1$. Then if $m_1\ne m_2$, the accelerations have to be unequal. But they can't be unequal during the time when the two rigid objects are in contact, so this is a contradiction.
A: 
What would happen both in terms of momentum and energy conservation?

When the ball hits the floor, the molecules of the ball will get real close to the molecules of the floor. At some point, they will start repelling each other. Whether the deformation at the point of contact significant or not, a sufficient reaction force will be acting on the ball for some period of time to stop it from going through the floor. 
At the moment the ball will stops, its kinetic energy will be converted to the potential energy of the deformed surfaces and, in case of a non-elastic collision, to heat. The momentum of the ball will be reduced to zero by the impulse of the reaction force. 
If the collision is elastic, the deformed surfaces will fully recover and their potential energy will be converted back to the ball's kinetic energy. As a result, the magnitude of the ball's velocity and momentum will be the same as they were just before the collision, while their direction will change to the opposite. The impulse of the reaction force, acting on the ball after the full stop, will be equal to the new momentum.
If the collision is not elastic, the recovered kinetic energy will be smaller than the kinetic energy before the collision. As a result, the magnitude of the velocity and the momentum after the collision will be smaller as well. The lost energy will be turned into heat. 
