In collision between two objects, kinetic energy is conserved only if

Analyze the question: We're asked under what condition kinetic energy is conserved in a collision between two objects.

Concept: Collisions fall into two main types:

• Elastic collision: Both momentum and kinetic energy are conserved. The objects bounce off each other with no permanent deformation, and no energy is lost as heat, sound, etc.
• Inelastic collision: Momentum is conserved, but some kinetic energy is converted into heat, sound, or deformation. Total kinetic energy after the collision is less than before.

(In every collision where no external force acts, momentum is conserved. Kinetic energy is conserved only in the elastic case.)

Checking each option:

• A. One of the objects was initially at rest: This doesn't decide whether KE is conserved. A moving ball can hit a stationary one and still lose energy as heat and sound. ✗
• B. Potential energy is converted to work: This has nothing to do with conservation of kinetic energy in a collision. ✗
• C. The collision is inelastic: In an inelastic collision, kinetic energy is not conserved. ✗
• D. The collision is elastic: By definition, kinetic energy is conserved. ✓

Answer: The correct option is D.

Tip: Remember "Elastic = Energy conserved." Momentum is conserved in all collisions, but kinetic energy is conserved only in elastic ones.