Question

In a perfectly elastic collision:
A. Both KE and momentum are conserved
B. Only KE is conserved
C. Only momentum is conserved
D. Neither KE nor momentum are conserved

Answer 1

Hint: A collision occurring between two bodies can be said to involve only internal forces if both the bodies together are considered to be a system. The momentum of a system changes due to external forces acting on it. If there is no deformation of the bodies during collision and there is no dissipation of energy in the form of sound or heat, then the kinetic energy of the system remains the same, that is, it is conserved.

Complete step by step answer:
During a collision between two bodies, if the two bodies are together considered to be a system, then it can be said that there are no external forces acting on the system and the two bodies colliding with each other give rise to only internal forces. The momentum of a system is changed only when external forces act on it. Hence, it can be said that there is no momentum change during a collision and therefore, the momentum is conserved.
Also, in an elastic conversion, there is no deformation of the bodies during the collision. If there is deformation, a part of the kinetic energy of the body is used for the purpose of the deformation and is stored as the potential energy. Also, in an elastic collision, there is no other dissipation of energy in the form of heat and sound. Hence, the kinetic energy of the system remains the same before and after the collision. Hence, it can be said that the kinetic energy of the system remains conserved during an elastic collision.
Therefore, the momentum and kinetic energy both are conserved in an elastic collision. Therefore, the correct option is A) both KE and momentum are conserved.

Note: Momentum is conserved in all collisions regardless of the collisions being elastic or inelastic. However, kinetic energy is only conserved in a perfectly elastic collision. In a perfectly inelastic collision, the two bodies join and stick together during the collision and remain stuck to form a single body after the collision that has the mass as the sum of the mass of the original two bodies.