Question

The total mechanical energy of a system is conserved if the forces that act on it are:

Answer 1

Hint: In order to answer this question, first we will discuss the nature of force that acts on the system, whose total mechanical energy is conserved. And then we will discuss the reason why the electrostatic force is conservative in nature.

Complete Step By Step Answer:
The total mechanical energy of a system is conserved if the forces that act on it are conservative in nature.
First and foremost, we must comprehend the concept of a conservative force, as well as when we refer to a force as being conservative in character. “Work performed by a force is considered to be conservative if it is independent of the path taken by its point of application and solely depends on the initial and final positions.” The following corollaries can be drawn from this statement:
(i) Work done by a conservative force in a full cycle (i.e. the path in which initial and final positions are the same) is always zero.
(ii) Work done against a conservative force is completely recoverable.
(iii) The conservative force never causes the system's energy to dissipate. When only conservative forces are present inside a system and no work is performed on the system by any external agent, the system's entire mechanical energy is preserved. This is commonly referred to as the principle of mechanical energy conservation.

Note:
There will be a change in the total mechanical energy of an object whenever work is done on it by an external force (or nonconservative force). There is no change in the overall amount of mechanical energy if only internal forces are at action (no work done by external forces).