Which of the following best describes the requirement of the law of conservation of energy in a closed system?

• A. The total kinetic energy of the system must always increase.
• B. Energy is only conserved when $m=0$.
• C. The total energy of the system remains constant over time.
• D. Energy can be created if it is balanced by an equal amount of energy destroyed elsewhere.

Answer: (C)

Verified step by step guidance

1. Understand that the law of conservation of energy states that within a closed system, energy cannot be created or destroyed, only transformed from one form to another.
2. Recognize that this means the total energy of the system remains constant over time, regardless of the changes in kinetic, potential, thermal, or other forms of energy within the system.
3. Note that the total kinetic energy does not have to always increase; it can increase or decrease as long as the total energy remains unchanged.
4. Acknowledge that the condition \( m = 0 \) (mass equals zero) is not related to the conservation of energy principle.
5. Reject the idea that energy can be created if balanced by destruction elsewhere, since energy conservation means total energy is constant, not that energy can be created or destroyed in any form.