1. Tardigrade
  2. Question
  3. Physics
  4. A force F(x) is conservative, if I. it can be derived from a scalar quantity V(x). II. it depends only on the end points. III. work done by F(x) in a closed path is zero. Which of the above statement(s) is/are correct?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A force $F(x)$ is conservative, if
I. it can be derived from a scalar quantity $V(x)$.
II. it depends only on the end points.
III. work done by $F(x)$ in a closed path is zero.
Which of the above statement(s) is/are correct?

Work, Energy and Power

Solution:

A force $F(x)$ is conservative, if it can be derived from a scalar quantity $V(x)$ by the relation given by equation, $\Delta V=-F(x) \Delta x$.
The work done by the conservative force depends only on the end points. This can be seen from the relation,
$W=K_{f}-K_{i}=U\left(x_{i}\right)-U\left(x_{f}\right)$
which depends on the end points.
The work done by this force in a closed path is zero. This is once again apparent from equation, $K_{i}+U\left(x_{i}\right)=K_{f}+U\left(x_{f}\right)$,
since $x_{i}=x_{f}$.
So, all statements are correct.