Final answer:
The total momentum of a two-body system in a collision remains constant when there are no external forces acting on the system. Momentum is conserved according to the principle of conservation of momentum. Kinetic energy may not be conserved if the collision is inelastic.
Step-by-step explanation:
When considering the total momentum of a two-body system in a collision, it is important to refer to the principle of conservation of momentum. In an isolated system where no external forces are acting, the total momentum before the collision must be equal to the total momentum after the collision. This is explained by the fact that momentum is a conserved quantity in the absence of external forces, meaning it cannot be created or destroyed, only transferred from one object to another.
In the scenarios provided, where two objects of equal mass collide and no external forces act on them, the correct statement about the collision is that: momentum is conserved, but kinetic energy may not necessarily be conserved, especially in inelastic collisions where objects stick together or deform, thereby dissipating some kinetic energy as heat or sound. However, without additional information on the type of collision (elastic or inelastic), we can definitively say that the total momentum remains constant.