Difficulty: Easy
Correct Answer: Metacentre (M) and centre of gravity (G)
Explanation:
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:
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:
Identify points: G (weight line of action), B (buoyancy centre), M (intersection of buoyant lines for small heel).Define GM = distance from G to M (positive if M is above G).Relate to righting arm: GZ ≈ GM * sin θ for small θ.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)
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