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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=-∫_⃗r₁^⃗r₂⃗F· d⃗r. 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:

Asked in JEE Main 22nd Jan 2nd Shift 2026 · Work from force and displacement vectors

• (1) Statement I is false but Statement II is true
• (2) Statement I is true but Statement II is false
• (3) Both Statement I and Statement II are false
• (4) Both Statement I and Statement II are true

Step-by-step solution

Why the other options are wrong

• (1) Comes from accepting that path choice changes the work; for a conservative force it never does.
• (2) Comes from confusing the work integral with the potential-energy change, which is the one carrying the minus sign.
• (4) Comes from accepting both the sign error and the path-dependence claim.

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