Question

There will be an increase in the potential energy of the system if the work is done upon the system by
A. any conservation of non-conservation force
B. a non-conservation force
C. a conservation force
D. none of these

Answer 1

Hint: The concepts of conservative and non-conservative forces are used. We will make use of the work-energy theorem to find the type of force. If, the work done equals a negative sign, then, it indicates that the work will be done on the system, if, in case, the work done equals a positive sign, then, it indicates that the work will be done by the system.
Formula used:
\[{{W}_{cons}}=-\Delta U\]

Complete step by step answer:
Let us understand the properties of the conservative forces.
The properties of the conservative forces are: The work done in the case of the conservative forces will be independent of the path chosen and the work done along a closed-loop will be zero. The work done by the conservative force only depends on the initial and final position of the system.
According to the work-energy theorem, the work done by the system will be equal to the negative of the change in the potential energy of the system. The expression for the same is as follows.
\[{{W}_{cons}}=-\Delta U\]
Where \[\Delta U\]represents the change in the potential energy of the system after doing the work.
If, in case there will be an increase in the change in the potential energy of the system after doing the work, then, the work will be done on that system.
\[\begin{align}
  & {{W}_{cons}}=-\Delta U \\
 & \Rightarrow {{W}_{cons}}=-(+\Delta U) \\
 & \Rightarrow {{W}_{cons}}=-\Delta U \\
\end{align}\]
Similarly, if, in case there will be decrease in the change in the potential energy of the system after doing the work, then, the work will be done by that system.
\[\begin{align}
  & {{W}_{cons}}=-\Delta U \\
 & \Rightarrow {{W}_{cons}}=-(-\Delta U) \\
 & \Rightarrow {{W}_{cons}}=+\Delta U \\
\end{align}\]
As there will be an increase in the potential energy of the system if the work is done upon the system by a conservation force, thus, the option (C) is correct.

Note:
As the conservative force defines the work done on/by the system in terms of the potential energy of the system, similarly, the non- conservative force defines the work done on/by the system in terms of the mechanical energy of the system. The conservative force is independent of the path chosen by the system to do work, whereas, the non- conservative force is dependent on the path chosen by the system to do work.