Work Energy Power

JEE Main level, single correct, medium

41 of 183

Question 41 of 183

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 :

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Answer: (A) Both Statement I and Statement II are false

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).

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