Work, Power and Energy Part 2

Concept:Work done by a force is path independent for conservative forces and path dependent for non-conservative forces.Formula:Work done by a variable force: $W = \int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}$For a conservative force: $W = -\Delta U = -\left(U_f - U_i\right)$Solution:Statement I says work done is $W = -\int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$. The correct definition is $W = \int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$ for any force. The negative sign only appears when writing work done by a conservative force in terms of potential energy: $W = -\Delta U$. Thus, Statement I has an incorrect minus sign. So Statement I is false.Statement II says for a conservative force, work done changes with the path. But for a conservative force, work done is path independent; it depends only on initial and final positions. Whether the object follows a straight line, curved path, or zig‑zag, the work done is the same between two points. Therefore, Statement II is also false.Both statements are false.Answer:Both Statement I and Statement II are false. Hence, option C is correct.