Question

For the given statements below, mark the correct option. Statement-I: Work done by a conservative force \( f \), from \( r_1 \) to \( r_2 \) is given by: \[ W = \int_{r_1}^{r_2} f \, dr. \] Statement-II: Work done by conservative force is path dependent.

• A. Statement-I and Statement-II is true
• B. Statement-I is true and Statement-II is false
• C. Statement-I is false and Statement-II is true
• D. Statement-I and Statement-II is false

Hint:

For a conservative force, the work done is independent of the path and depends only on the initial and final points.

Answer 1

The Correct Option is D

Step 1: Analyze Statement I.
Statement I is incorrect. The work done by a conservative force is independent of the path taken, and it depends only on the initial and final positions. The correct expression for work done by a conservative force is: \[ W = -\int_{r_1}^{r_2} f \, dr. \] Step 2: Analyze Statement II.
Statement II is incorrect. Work done by a conservative force is path-independent, meaning it depends only on the initial and final positions, not the specific path taken. Step 3: Conclusion.
Both statements are false. Final Answer: \[ \boxed{\text{Statement-I and Statement-II is false.}}. \]