Given below are two statements :\ Statement I: An object moves from position $r_1$ to position $r_2

Question

Given below are two statements :\ Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int_{r_1}^{r_2} \vec{F} \cdot \overrightarrow{d r}$.\ Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.\ In the light of the above statements, choose the correct answer from the options given below :

Professor PC Thomas Classes · Answer

Statement I is false because the work done by a force is defined as the positive integral $W = \int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$. The negative integral represents the change in potential energy ($\Delta U = -W$). Statement II is also false because the defining characteristic of a conservative force is that the work done by it is strictly path-independent and depends only on the initial and final positions.