Which of the following quantities remains conserved for a system which is subjected to a conservative force?

The correct answer is Total mechanical energy.

Key Points

• Total mechanical energy (sum of kinetic and potential energy) remains conserved in a system subjected to a conservative force.
• In a conservative force field, the work done by the force only depends on the initial and final positions, not on the path taken.
• This conservation implies that any change in potential energy of the system is exactly balanced by a change in kinetic energy.
• Examples of conservative forces include gravitational force, electrostatic force, and spring force.

Additional Information

• Conservative Force
  • A force is considered conservative if the work it does on a particle moving between two points is independent of the path taken.
  • Examples include gravitational force, electrostatic force, and the elastic force in springs.
• Mechanical Energy
  • Mechanical energy is the sum of kinetic energy (energy due to motion) and potential energy (energy due to position).
  • In the absence of non-conservative forces, the total mechanical energy of a system remains constant.
• Non-Conservative Forces
  • Non-conservative forces, such as friction and air resistance, cause energy to be transferred out of the system, often as heat.
  • These forces do not have the property of path independence.
• Energy Conservation
  • Energy conservation is a fundamental principle stating that energy cannot be created or destroyed, only transformed from one form to another.
  • In a closed system not subjected to external forces, the total energy remains constant.