Question

The potential energy of a system increases if work is done

A. Upon the system by a non-conservative force

B. By the system against a conservative force

C. By the system against a non-conservative force

D. Upon the system by a conservative force

Answer 1

Hint: We use and analyze the conservation force formula to solve this required solution. A conservative force only depends on the object's location. We will draw a conclusion from the equation the work done thus obtained. 

Complete step by step solution:

We know, The conservation force formula is,

$F = \dfrac{{ - dU}}{{dr}} $

$\Rightarrow  - dU = F \times dr$

Where,

\[ \Rightarrow  - dU = {W_{{\text{conservative}}\,{\text{force}}}}\]

When the system operates against any conservative force, the potential energy changes and the rate of the potential energy change is negative in terms of position, if a conservative force works upon this system.

Hence, the potential energy of a system increases if work is done by the system against a conservative force. The correct option is (B).

Additional information:
Conservative force: A conservative force is a force with the property that is independent of the way the total function in moving a particle between two points. In the same way, if a particle is in a shuttered loop, the total effort carried out by a conservative force (the amount of the force acting along the direction by the displacement) is zero.

Note: Conservative force, in the physical sphere, any force, for example a gravitational force between Earth and another mass, the work of which is only determined by the final movement of the object. Only conservative forces may describe stored energy or potential energy.