Which is the type of collision in which both the linear momentum and the kinetic energy of the system remain conserved?

The correct answer is Elastic collision.

Key Points

• An elastic collision is a type of collision in which both linear momentum and kinetic energy of the system are conserved.
• In such collisions, there is no loss of kinetic energy as the objects rebound without deformation or generation of heat.
• Elastic collisions commonly occur at the atomic or molecular level, such as in gas molecules during thermal motion.
• In macroscopic systems, perfect elastic collisions are rare but can be approximately observed in scenarios like collisions between billiard balls or steel balls.
• The mathematical equations for conservation in elastic collisions are derived from Newton’s laws of motion and the principle of energy conservation.

Additional Information

• Linear Momentum Conservation:
  • The total momentum of the system before and after the collision remains the same.
  • This principle is expressed as: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where m₁ and m₂ are masses, and u and v are initial and final velocities.
• Kinetic Energy Conservation:
  • The total kinetic energy of the system is conserved during the collision.
  • This can be written as: ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂².
• Inelastic Collision:
  • In an inelastic collision, only the linear momentum is conserved, while kinetic energy is not conserved due to energy loss in the form of heat, sound, or deformation.
  • Example: A car crash where vehicles stick together after impact.
• Destructive Collision:
  • It is a term used to describe collisions that result in the significant loss of energy and deformation of objects.
  • It is not a standard term in physics for classifying collisions.
• Real-Life Examples of Elastic Collisions:
  • Collision of gas particles in a closed container.
  • Interaction between two steel balls in Newton’s cradle.