Stability: GM and metacenter Practice Questions

1. The metacentric height (GM) of a vessel is best described as the distance between the:

• A.Center of gravity (G) and the metacenter (M)✓
• B.Center of buoyancy (B) and the metacenter (M)
• C.Keel and the center of gravity (G)
• D.Center of buoyancy (B) and the center of gravity (G)

Why: GM is the vertical distance between the ship's center of gravity (G) and the metacenter (M). A positive GM (M above G) indicates initial stability, while a negative GM indicates an unstable vessel.

2. A vessel has a GM of zero. Which statement best describes the vessel's condition?

• A.The vessel is in neutral equilibrium and will remain at any angle of heel✓
• B.The vessel is stable and will return quickly to upright
• C.The vessel is unstable and will capsize immediately
• D.The vessel has a loll and will flop to one side

Why: When GM equals zero, the metacenter coincides with the center of gravity, producing neutral equilibrium — the vessel will neither return to upright nor continue to heel further, remaining at whatever angle it is placed.

3. Which formula correctly expresses the relationship between GM, KB, BM, and KG?

• A.GM = KB + BM − KG✓
• B.GM = KG − KB − BM
• C.GM = BM − KB + KG
• D.GM = KB − BM + KG

Why: Since KM = KB + BM and GM = KM − KG, it follows that GM = KB + BM − KG. All distances are measured vertically from the keel (K). This relationship is fundamental to stability calculations.

4. A vessel loads a heavy cargo on deck, raising the center of gravity. What happens to KM (height of metacenter above keel) as a result?

• A.KM remains essentially unchanged because it depends on hull geometry, not cargo placement✓
• B.KM rises because additional weight raises the center of buoyancy
• C.KM falls because the metacenter follows the center of gravity
• D.KM increases because the vessel sinks deeper, raising BM

Why: KM = KB + BM is a function of the vessel's hull form and waterplane geometry, not where cargo is placed. While loading cargo changes the draft (slightly altering KB and BM from the hydrostatic tables), KM does not follow G — the reduced GM is because G has risen, not because M has fallen.

5. A 'stiff' vessel with a large positive GM will characteristically:

• A.Roll quickly with a short, jerky motion that can cause cargo to shift and stress rigging✓
• B.Roll slowly and gently with a long period, reducing structural stress
• C.Have poor initial stability but excellent large-angle stability
• D.Be prone to capsizing in beam seas due to rapid roll reversal

Why: A stiff vessel has a very large GM, producing large righting moments at small angles. This results in a short rolling period and rapid, jerky rolls that increase dynamic loads on cargo lashings, cranes, and crew safety, even though the vessel is technically very stable.