Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202622 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Evening Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2026 · 22 January · Evening Shift · Physics · Work, Power and Energy

Given below are two statements : Statement I : An object moves from...

Given below are two statements :
Statement I: An object moves from position r1r_{1} to position r2r_{2} under a conservative force field F⃗\vec{F}. The work done by the force is W=−∫r1r2F⃗⋅dr→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 :

Options

  1. ABoth Statement I and Statement II are false
  2. BStatement I is false but Statement II is true
  3. CStatement I is true but Statement II is false
  4. DBoth Statement I and Statement II are true

Correct answer

A. Both Statement I and Statement II are false

Step-by-step solution

Statement I:
The work done by a force F⃗\vec{F} during a displacement from r⃗1\vec{r}_1 to r⃗2\vec{r}_2 is defined as W=∫r1r2F⃗⋅dr⃗W = \int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}.
The expression given in the statement, W=−∫r1r2F⃗⋅dr⃗W = -\int_{r_1}^{r_2} \vec{F} \cdot d\vec{r}, is the definition of the change in potential energy (ΔU=−W\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).
Practice Work, Power and Energy on Quantrex Academy →

More from Work, Power and Energy

All Work, Power and Energy questions Full Work, Power and Energy list All JEE Main PYQs