Question

Which of the following statements is not related to conservative force?
a) Work done in closed path is zero
b) Work done is recoverable
c) Path independent
d) Path dependent

Answer 1

In order to answer the above question we first need to understand the conservative and non-conservative forces. From the word conservative we get some hint that it basically involves conservation. More precisely it speaks about the conservation of energy. Hence accordingly we will be able to select the correct alternatives from those provided.
Formula used:
${{W}_{\left( ABC \right)}}={{W}_{\left( ADC \right)}}$

Complete step-by-step solution:
A force is conservative if the work done by the force in displacing a particle from one point to another is independent of the path followed by the particle and only depends on the initial and the final position. To understand this let us consider a particle moving from point A to C, via D and B along two different paths.

The work done in moving the particle from along the two different path is given by,
${{W}_{\left( ABC \right)}}={{W}_{\left( ADC \right)}}$
Similarly if the force is path dependent then we call it a non conservative force. Hence from the above information we can conclude that conservative force is not path dependent. Therefore the correct answer of the above question is option d.

Note: It is to be noted that in case of work done against a conservative force, the mechanical energy of the system is conserved. Hence we can imply that work done is recoverable. In a closed path, the initial and final position being the same as the work done in the closed path is zero.