Question

The graph of potential energy ($U$) Vs position ($X$) is shown in the figure given below. Select the correct order regarding the equilibrium state of $\left(\text{a}\right),\left(\text{b}\right)$ & $\left(\text{c}\right)$.

• A. Stable, Unstable, Neutral
• B. Unstable, Stable, Neutral
• C. Neutral, Stable, Unstable
• D. Neutral, Unstable, Stable

Answer 1

The correct option is B Unstable, Stable, Neutral

For respective positions of particle:
(a) If particle displaced on either side w.r.t it's equilibrium position, then potential energy ($U$) will be decrease on both sides. So, it will tend to move in both directions if displaced slightly.
Hence, UNSTABLE equilibrium position.

(b) If particle displaced on either side w.r.t it's equilibrium position, then potential energy ($U$) will be increase on both sides. So, it will tend to come back to original position, if displaced slightly towards any side.
Hence, STABLE equilibrium position.

(c) If particle is displaced on any side w.r.t it's equilibrium position, then potential energy ($U$) remains almost same. So, it doesn't make any sense for particle to move towards any side. Hence, NEUTRAL equilibrium position.

Hence option (b) is the correct answer