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 occur where the derivative of the potential energy with respect to x is zero, i.e., where the force is zero.
2. Step 2: From the graph, there are three points where the potential energy is at a minimum or maximum. The point at the minimum corresponds to a stable equilibrium, while the points at the maxima correspond to unstable equilibria.
3. Step 3: Therefore, the particle has three equilibrium points, with one stable and two unstable.