Stability of floating bodies — classify the equilibrium A floating body is given a small angular displacement. If it does not return to its original position and, instead, heels further away, what is the correct classification of its equilibrium state?

Introduction / Context:
The response of floating bodies (ships, buoys) to small angular disturbances is characterized by metacentric height and the resulting restoring or overturning moments. Correctly identifying stable, neutral, or unstable equilibrium is crucial for naval architecture and safety.

Given Data / Assumptions:

• Body floats in a fluid and is slightly heeled.
• Observation: it moves farther away from the original position rather than returning.
• Small-angle behavior is considered (initial stability).

Concept / Approach:
Equilibrium types: (1) Stable — a small angular displacement generates a restoring moment that brings the body back; (2) Neutral — no restoring or overturning moment, so it remains indifferent at the new angle; (3) Unstable — an overturning moment increases the heel. The described behavior (heels further away) clearly matches unstable equilibrium.

Step-by-Step Solution:
Apply a small heel to the floating body.Observe the direction of the resultant moment due to displaced buoyancy vs. weight line of action.If the moment increases the heel, the equilibrium is unstable.Therefore, select “Unstable equilibrium.”

Verification / Alternative check:
For initial stability, metacentric height GM > 0 → stable; GM = 0 → neutral; GM < 0 → unstable. The given behavior corresponds to GM < 0, confirming the classification as unstable.

Why Other Options Are Wrong:

• Neutral equilibrium: would stay at the new position, not move further away.
• Stable equilibrium: would return toward upright.
• “Metacentric equilibrium only at zero heel” is not a standard classification and does not reflect the observed behavior.

Common Pitfalls:

• Mislabeling neutral as unstable; neutral implies neither restoring nor overturning moment.

Final Answer:
Unstable equilibrium