When a body is slightly tilted, it is found that its centre of gravity is slightly raised. What is the state of equilibrium of the body?

Analyze the question: A body is slightly tilted, and its centre of gravity (C.G.) rises. We need to name the type of equilibrium.

Concept: There are three states of equilibrium, and each depends on what happens to the C.G. after a small displacement:

• Stable equilibrium: The C.G. is raised when the body is displaced. The body's weight then produces a restoring torque, so it returns to its original position. Example: a cone resting on its base, or a ball in a bowl.
• Unstable equilibrium: The C.G. is lowered when the body is displaced. The weight produces a torque that topples the body further. Example: a cone balanced on its tip.
• Neutral equilibrium: The C.G. stays at the same height. The body stays in its new position. Example: a cone lying on its side, or a ball on a flat table.

Solution:

1. The body is tilted slightly.
2. Its C.G. rises, so its potential energy increases (PE = mgh).
3. The body therefore tends to return to the position of lowest potential energy, which is its original position.
4. A body that returns to its original position after a small displacement is in stable equilibrium.

Answer: B (stable)

Tip: Remember it as "Raised = Returns = Stable". If the C.G. goes up, the body comes back. If it goes down, the body falls over (unstable). If the height doesn't change, the equilibrium is neutral.