Question

U(x) − x curve of one dimensional conservative force is shown. Three points A, B and C are marked on the curve. The correct pairing of the points with the type of equilibrium they show on the curve is :

• A. A → Unstable, B → Stable, C → Neutral
• B. A → No equilibrium, B → Unstable, C → Stable
• C. A → Neutral, B → Unstable, C → Stable
• D. A → Neutral, B → Stable, C → Unstable

Answer 1

Answer: (B)

A → No equilibrium, B → Unstable, C → Stable

Answer 2

At A, ≠ 0 hence F ≠ 0 thus showing no equilibrium. At B, if particle is displaced along positive direction, slope become negative and F $\left( = - \frac { d U } { d x } \right)$ becomes positive indicating unstable equilibrium. At C, conditions are reverse that of at B i.e., unstable equilibrium.