Question

Conservative forces are those forces for which

• A. $\int \overrightarrow{F}\cdot d\overrightarrow{r}=0$
• B. $\int \overrightarrow{F}\cdot d\overrightarrow{r}\ne 0$
• C. The work done depends upon the path
• D. Only the momentum remains constant

Answer 1

The correct option is A $\int \overrightarrow{F}\cdot d\overrightarrow{r}=0$

A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path. Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.

Hence, work done in close loop is $\oint F.dr=0$