Given below are two statements :
Statement I : An object moves from position r₁ to position r₂ under a conservative force field F. The work done by the force is W = -∫ $\vec{F}.\vec{dr}$ from r₁ to r₂.
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

Question

Given below are two statements :

Statement I : An object moves from position r₁ to position r₂ under a conservative force field F. The work done by the force is W = -∫ $\vec{F}.\vec{dr}$ from r₁ to r₂.

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

G1 Physics · Accepted Answer

Statement I is false. Work done by a force is W = ∫ F⃗·dr⃗ from the initial position to the final position. The negative sign appears in the relation between work done by a conservative force and potential-energy change: W(conservative) = -ΔU. Therefore the integral written in Statement I with an extra negative sign is incorrect. Statement II is also false. For a conservative force, the work done depends only on the initial and final positions and is independent of the path. Thus both statement…