Conservative Force and Work – 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:

Assertion (A) states the definition of a conservative force: the work done in a closed loop is zero.

Reason (R) states a key property of conservative forces: their work is path-independent. Path independence directly implies that the work done in any round trip (closed path) is zero, thus (R) correctly explains (A).

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): Work done by a force is always same in all inertial frame of references. Reason (R): Work is an invariant physical quantity.  
2. The kinetic energy acquired by a mass \(m\) in travelling distance \(d\), starting from rest, under the action of a constant force is directly proportional to: (1994)
3. Assertion (A): The work done during a round trip is always zero. Reason (R): No force is required to move a body in its round trip.
4. Assertion (A): The sum of potential and kinetic energy for a system of moving objects is conserved only when no net external force acts on the objects Reason (R): If no nonconservative force acts on a system of objects, the work done by external forces on a system of objects is equal to change in potential energy plus change in kinetic energy of the system.
5. Assertion (A): Kinetic energy of a system can be increased without applying any external force on the system. Reason (R): If external forces are absent then work done by internal forces is equal to change in kinetic energy.