Work done by conservative force – Rankers Physics

Potential Energy & Equilibrium: Practice Problem & Solution

Assertion (A): If in a round trip work done by a force is zero then force is conservative. Reason (R): Work done by conservative force field is independent of path.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Potential Energy & Equilibrium. Understanding the underlying formula is key to arriving at the correct answer below:

A conservative force is defined by two equivalent properties: work done in a closed loop is \(0\) and work done is path-independent. If \(W_{\text{round_trip}} = 0\), the force is conservative. \(W_{\text{conservative}} = 0\) for a round trip because it is path-independent, meaning \(W_{A to B} = -W_{B to A}\). Thus, Reason (R) correctly explains Assertion (A).

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