Which of the following statements describes a body in a stable equilibrium correctly?

Analyze the question: We need to identify which situation shows stable equilibrium.

Concept: There are three types of equilibrium:

• Stable equilibrium: When the body is slightly displaced, it returns to its original position. Its centre of gravity rises when displaced, so gravity pulls it back.
• Unstable equilibrium: When slightly displaced, the body moves further away from its original position. Its centre of gravity falls when displaced.
• Neutral equilibrium: When displaced, the body stays in its new position. Its centre of gravity stays at the same height.

Examine each option:

• A. A person walking on a tight-rope: The slightest tilt makes the person fall off. The centre of gravity is above the support, so this is unstable.
• B. A ball on a smooth horizontal table: If you push the ball, it simply rolls to a new position and stays there. The height of its centre of gravity does not change, so this is neutral.
• C. A ball resting on an inverted hemispherical bowl: The ball sits on top of a curved surface. A small push makes it roll down and away, and its centre of gravity falls, so this is unstable.
• D. A ball in the middle of a hemispherical bowl: The ball rests at the lowest point of the bowl. If displaced up the side, its centre of gravity rises, and gravity pulls it back to the bottom. This is stable.

Answer: The ball in the hemispherical bowl is in stable equilibrium.

Exam tip: Picture the ball in a valley (stable), on a hilltop (unstable), or on a flat plain (neutral). In a valley, the ball rolls back after a push, so it is stable.