JEE Main 2026 — Jan 22, Shift 2 — Physics solution

JEE Main2026Jan 22, Shift 2Physics

Given below are two statements :

Statement I : An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $F$ . The work done by the force is $W = - \int_{r_{1}}^{r_{2}} F \cdot d r$ .

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 :

A
Both Statement I and Statement II are true
B
Statement I is false but Statement II is true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false

Solution

The correct definition is $W = \int_{r_{1}}^{r_{2}} F \cdot d r$ (no negative sign). The negative sign appears when relating work to change in potential energy: $W = - Δ U$ . So Statement I is incorrect.

Statement II is incorrect because, for a conservative force, the work done is path-independent — that is the defining property of conservative forces.

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