Question

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?

• A. Only I
• B. Both I and III
• C. Only II
• D. I, II and III

Answer 1

Answer: (D)

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.