Metacentric Height (GM) Practice Questions

1. A vessel with a very large positive GM is described as:

• A.Tender, with a long slow rolling period
• B.Stiff, with a short snappy rolling period✓
• C.Neutral, with no tendency to return upright
• D.Loll-prone, with an angle of static equilibrium off centerline

Why: A large GM produces a large righting moment at small angles, causing the vessel to snap back quickly — a stiff ship with a short rolling period. While safer than a tender ship, very stiff ships can impose high dynamic loads on cargo and crew.

2. A vessel has a very small but still positive GM. This vessel is best described as:

• A.Stiff, likely to snap-roll
• B.Tender, with a long slow rolling period and reduced comfort margin✓
• C.Neutrally stable with zero righting moment
• D.In a state of loll

Why: A small positive GM means the righting moment is weak. The vessel rolls slowly (long period) and is called tender. Although technically stable, the small margin increases the risk of a dangerous list or capsize if additional weight is added high.

3. The rolling period formula T = 0.44 B / sqrt(GM) shows that as GM increases, the rolling period:

• A.Increases — the ship rolls more slowly
• B.Decreases — the ship rolls more quickly✓
• C.Stays the same because beam dominates
• D.Becomes unpredictable

Why: Since GM appears in the denominator under a square root, a larger GM reduces the rolling period — the ship rolls faster and snappier (stiff). A smaller GM increases the period — the ship rolls slowly (tender).

4. A vessel's rolling period is measured at 18 seconds. Compared to the same vessel with a period of 10 seconds, the 18-second ship has:

• A.A larger GM and is more stable
• B.A smaller GM and is more tender✓
• C.The same GM but a wider beam
• D.A negative GM

Why: Longer rolling period means smaller GM. A small GM means less righting moment — the vessel is tender. The 18-second roll is a warning sign of reduced initial stability; investigation and corrective action may be required.

5. In the inclining experiment formula GM = (w x d) / (W x tan θ), what does 'W' represent?

• A.The weight of the inclining mass moved
• B.The vessel's displacement at the time of the experiment✓
• C.The width of the vessel at the waterline
• D.The moment to trim one inch

Why: W is the total displacement (weight) of the vessel during the experiment. The heeling moment (w x d) is divided by (W x tan θ) to give GM. Accurate displacement requires careful draft readings and density measurement during the experiment.