A body was slightly displaced from its equilibrium position. Which one of the following is a condition for its stable equilibrium

Analysis

The question asks for the condition that defines stable equilibrium when a body is slightly displaced from its original position.

Concept Explanation

Equilibrium occurs when the net force acting on a body is zero. However, there are three types of equilibrium based on how the body reacts to a displacement:

1. Stable Equilibrium: When a body is slightly displaced and released, it tends to return to its original position. In this state, the body's potential energy is at a minimum. When you displace it, you are essentially "lifting" it against gravity or a restoring force, which causes its potential energy to increase. Because the system naturally wants to return to the lowest energy state, it moves back to its original position.
2. Unstable Equilibrium: When a body is slightly displaced and moves further away from its original position. Here, the potential energy is at a maximum.
3. Neutral Equilibrium: When a body is displaced and stays in its new position. The potential energy remains constant.

Step-by-Step Solution

1. Identify the state: We are looking for stable equilibrium.
2. Analyze the energy change: When a body in stable equilibrium (like a ball at the bottom of a bowl) is pushed slightly, it rises to a higher position.
3. Relate to Potential Energy ($PE = mgh$): As the body rises, its height ($h$) increases. Since potential energy is directly proportional to height, the potential energy of the body must increase.
4. Conclusion: The increase in potential energy creates a "restoring force" that pulls the body back down to the point of minimum potential energy (the equilibrium position).

Identifying the Answer

• Option A and C (Kinetic Energy) are incorrect because kinetic energy relates to motion, not the stability of the position.
• Option D (Increase in height) is a consequence of the displacement, but the fundamental physical condition that defines the stability is the increase in potential energy.
• Option B is the correct scientific description of the state of the body after displacement.

Exam Tip

Think of a ball in a bowl:

• Stable: Ball at the bottom. If you push it, it goes up (Potential Energy increases) and rolls back down.
• Unstable: Ball balanced on top of an inverted bowl. If you push it, it falls away (Potential Energy decreases).
• Neutral: Ball on a flat table. It just stays wherever you push it.