Metacentric height (GM) is defined as the distance between which two points of a floating body for small-angle stability analysis?

Introduction / Context:
Initial stability of ships and floating structures is quantified by the metacentric height GM. A positive GM indicates a restoring moment for small heel angles. Designers track GM for safety, comfort, and performance under load changes and free-surface effects.

Given Data / Assumptions:

• Small-angle heel so that the concept of a single metacentre M is valid.
• Homogeneous fluid; hydrostatic buoyancy principles apply.
• Rigid body, no flooding or free-surface sloshing effects included.

Concept / Approach:

Metacentric height GM is defined as the algebraic distance between the metacentre M and the centre of gravity G: GM = BM − BG. The sign of GM governs stability: GM > 0 yields a righting couple; GM < 0 yields instability. While BM (metacentric radius) depends on geometry of the waterplane, BG depends on loading and ballast.

Step-by-Step Solution:

Verification / Alternative check:

Inclining experiment measures GM experimentally by shifting a known mass and observing equilibrium angle; result accords with the GM definition above.

Why Other Options Are Wrong:

(a) GB is not GM; (c) BM is the metacentric radius, not GM. (d) and (e) do not state the correct definition for GM.

Common Pitfalls:

Confusing GM with BM; remembering that GM depends on both BM and BG is crucial for design changes.

Final Answer:

Metacentre (M) and centre of gravity (G)