Floating Bodies — Point About Which Small Oscillations Occur When a floating body in a liquid is given a small angular displacement, it oscillates about a specific point known as the:

Introduction:
Stability of floating bodies is fundamental to naval architecture and hydraulic structures. Small angular disturbances lead to restoring or overturning moments depending on the relative positions of characteristic points within the body–fluid system.

Given Data / Assumptions:

• Small angular displacement (linearized stability analysis).
• Homogeneous, incompressible liquid; body floating partially submerged.
• No waves or dynamic sloshing considered.

Concept / Approach:
For small heel angles, the line of action of buoyant force shifts because the submerged volume changes shape. The point about which the buoyant force line appears to rotate is the metacentre. If metacentre M lies above the centre of gravity G, the body experiences a restoring couple and is statically stable.

Step-by-Step Solution:
Identify key points: centre of gravity G (fixed in body), centre of buoyancy B (centroid of displaced liquid), and metacentre M.On heeling, B shifts; the new vertical through B intersects the original vertical at M.Oscillation for small disturbances occurs about M; stability requires GM > 0 (M above G).

Verification / Alternative check:
Model tests show righting moment proportional to GM * sin(theta) for small angles; oscillations centre on the metacentre under linear assumptions.

Why Other Options Are Wrong:
Centre of pressure applies to distributed pressure on surfaces; centre of buoyancy is the force application point but not the oscillation centre; centre of gravity is a body-fixed point, not the hydrodynamic pivot.

Common Pitfalls:
Confusing B with M; assuming large-angle behavior follows small-angle linear theory; neglecting free-surface effects on stability.

Final Answer:
metacentre