In an elastic collision, momentum is conserved as well as well as?

Step 1: Analyze the question The question asks what quantity is conserved in an elastic collision in addition to momentum.

Step 2: Explain the concept Collisions fall into two main types:

• Elastic collision: Both momentum and kinetic energy are conserved. The objects bounce off each other and no kinetic energy is lost as heat, sound, or deformation. Collisions between gas molecules and between billiard balls are close to this ideal.
• Inelastic collision: Momentum is conserved, but some kinetic energy is converted to other forms such as heat, sound, or deformation. In a perfectly inelastic collision, the bodies stick together.

Momentum is conserved in all collisions, provided no external force acts on the system. Kinetic energy is conserved only in elastic collisions.

Step 3: Work through the options

• A. Velocity: Not conserved. Velocities of the bodies usually change after a collision. Only the total momentum, m₁u₁ + m₂u₂, stays the same.
• B. Kinetic energy: Conserved. ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂².
• C. Potential energy: Not the relevant quantity. Potential energy is not what defines an elastic collision.
• D. Speed: Not conserved in general. Individual speeds change unless the masses are equal and the collision is head-on with one body at rest.

Step 4: Answer The quantity conserved along with momentum in an elastic collision is kinetic energy, which is option B.

Exam tip: Remember "Elastic = Energy kept." Momentum is conserved in every collision, but kinetic energy is conserved only if the collision is elastic. If a question mentions bodies sticking together or energy lost as heat or sound, it is inelastic.