Question

In one dimensional elastic collision of equal masses, the velocities are interchanged. Can velocities in a one-dimensional collision be interchanged if the masses are not equal?

Answer 1

No, because the linear momentum will not be conserved. For example, consider the one-dimensional collision of mass m with velocity 2v and mass 2m with velocity v before the collision. Total momentum = m.2v+2m.v = 4mv. Had the velocities been interchanged after the collision, final momentum of the system would be = m.v+2m.2v = 5mv, which is not according to the principle of conservation of the linear momentum. So the velocities, in this case, will not be interchanged.