Q61 / 75 · JEE Main 2026 (22 January Shift 2) · Physics
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 :
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 :
- Correct answerABoth Statement I and Statement II are false
- BStatement I is false but Statement II is true
- CStatement I is true but Statement II is false
- DBoth Statement I and Statement II are true
Solution
Statement I:
The work done by a force $\vec{F}$ during a displacement from $\vec{r}_1$ to $\vec{r}_2$ is defined as $W = \int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$.
The expression given in the statement, $W = -\int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$, is the definition of the change in potential energy ($\Delta U = -W$), not the work done by the force itself.
Thus, Statement I is false.
Statement II:
By definition, a conservative force is one for which the work done in moving an object between two points is independent of the path taken.
It only depends on the initial and final positions.
Therefore, the claim that work done changes with the path for a conservative force is false.
Since both statements are false, the correct option is (1).
The work done by a force $\vec{F}$ during a displacement from $\vec{r}_1$ to $\vec{r}_2$ is defined as $W = \int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$.
The expression given in the statement, $W = -\int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}$, is the definition of the change in potential energy ($\Delta U = -W$), not the work done by the force itself.
Thus, Statement I is false.
Statement II:
By definition, a conservative force is one for which the work done in moving an object between two points is independent of the path taken.
It only depends on the initial and final positions.
Therefore, the claim that work done changes with the path for a conservative force is false.
Since both statements are false, the correct option is (1).
Hence, the correct answer is option: 'A'.