Which force has zero work done around any closed path?

Which force has zero work done around any closed path?

• A. Non-conservative force
• B. Natural force
• C. Virtual force
• D. Conservative force

Answer: (D)

The main idea is that a conservative force is path-independent: the work it does depends only on the endpoints, not on the route taken. If you can express the force as F = -∇U, then the work along any path from point A to point B is W = U(A) - U(B). For a closed loop, you start and end at the same point, so U(A) - U(A) = 0, and the total work around the loop is zero. This property is what makes conservative forces unique in this context. Non-conservative forces, such as friction, have work that depends on the path, so they generally do nonzero work around a closed path. The terms natural force or virtual force aren’t standard descriptors for this property, so they don’t guarantee zero work around a loop.

The main idea is that a conservative force is path-independent: the work it does depends only on the endpoints, not on the route taken. If you can express the force as F = -∇U, then the work along any path from point A to point B is W = U(A) - U(B). For a closed loop, you start and end at the same point, so U(A) - U(A) = 0, and the total work around the loop is zero.

This property is what makes conservative forces unique in this context. Non-conservative forces, such as friction, have work that depends on the path, so they generally do nonzero work around a closed path. The terms natural force or virtual force aren’t standard descriptors for this property, so they don’t guarantee zero work around a loop.