Question

For a conservative force F, all if the following are correct except
A. there exists an associated potential energy function.
B. the line integral of F between points A and B by way of point C is independent of point C.
C. the line integral of F around a closed path is zero.
D. the line integral of F with limits A and B is independent of the order of the limits.
E. the force F must be the net force including the internal force.

Answer 1

From the definition of the Conservative forces, the line integral of the force or work done by the force is independent of the path, it only dependeds upon the position of the points. For conservative forces the the curl of the force is zero, so we can write it as the gradient of a function, and this function is known as the potential energy function.

From above these properties we see that option A, B and option C are correct.

For option C when we take integral from point A to B and the take integral from point B to A, as we have seen the line intergral of conservative force only depends upon the points and here initial and final point are same, like point A to A, the integral will be equal to zero.

For option D as in option C from point A to B and the B to A intergration has overall value of zero,that means, integral from A to B has same value as integral from B to A, but with the opposite sign.

So, the line integral is not independent of order of integration. This option is wrong. Because change of sign in work done changes who performed the work.

Option E is correct as F is the net value of the force including internal forces.

Example of conservative force are gravitational force, electrostatic force.