Question

The following figure shows the variation of potential energy V (x) of a particle with distance x. The particle has:

• A. Two equilibrium points, one stable another unstable
• B. Two equilibrium points, both stable
• C. Three equilibrium points, one stable two unstable
• D. Three equilibrium points, two stable one unstable

Hint:

To identify stable and unstable equilibrium points, check the curvature of the potential energy graph: minima correspond to stable equilibria and maxima correspond to unsta ble equilibria.

Answer 1

The Correct Option is C

1. Step 1: Equilibrium points happen when the potential energy's derivative regarding x is zero, meaning the force is zero.
2. Step 2: The graph shows three points of potential energy minima or maxima. The minima represent stable equilibrium, and the maxima represent unstable equilibria.
3. Step 3: Thus, the particle has three equilibrium points: one stable and two unstable.