Fluid Mechanics – Stability of Floating Bodies When a floating body is given a very small angular displacement and it moves to a new position and then remains at rest in that new position, the body is said to be in which type of equilibrium?

Introduction:
In hydrostatics, the stability of floating bodies is discussed using three standard categories of equilibrium: stable, unstable, and neutral (also called indifferent). The question tests recognition of the precise definition of neutral equilibrium for a floating body after a small angular displacement.

Given Data / Assumptions:

• Body is floating in a liquid.
• A small angular displacement is applied.
• After displacement the body occupies a new position and then remains at rest there.

Concept / Approach:

Equilibrium of a floating body is judged by metacentric height GM, where G is the center of gravity and M is the metacenter. The nature is decided as: stable if GM > 0, unstable if GM < 0, and neutral if GM = 0. In neutral equilibrium the restoring moment is zero; hence the body has no tendency to return to the original position or move further away. It simply stays in the new position reached by the small disturbance.

Step-by-Step Solution:

Verification / Alternative check:

For neutral equilibrium, small rotations do not change the potential energy to first order. The waterline and buoyant force adjust to pass through the center of gravity without producing a net moment. This matches the described behavior.

Why Other Options Are Wrong:

Stable: GM > 0 would create a restoring moment, returning the body to its original position, which is not described.Unstable: GM < 0 would lead to an overturning moment that increases angular displacement, also not described.Metastable: Not a standard classification for hydrostatic equilibrium of floating bodies in this context.Indifferent: Synonym of neutral; included as a distractor to test terminology, but the canonical term is neutral.

Common Pitfalls:

Learners sometimes confuse neutral with stable, assuming “remains at rest” means it returns. The keyword is “remains at rest in the new position,” not in the original one. Also, mixing up the sign of GM is common.

Final Answer:

neutral