Question 54

The Correct Answer is B **Explanation for Option B (The vessel possesses neutral stability):** Stability in vessels is fundamentally determined by the relationship between the Metacentric Height (GM) and the vessel's vertical center of gravity (G) and its metacenter (M). The metacentric height (GM) is calculated as: $$GM = KM - KG$$ * $KG$ is the height of the center of gravity above the keel (K). * $KM$ is the height of the metacenter above the keel (K). If the problem states that $KG$ is equal to $KM$: $$KG = KM$$ Substituting this into the GM formula: $$GM = KM - KM$$ $$GM = 0$$ When the metacentric height ($GM$) is zero, the vessel possesses **neutral stability**. This means that when the vessel is slightly heeled, the center of gravity (G) coincides exactly with the metacenter (M). The righting lever ($GZ$) is zero, and the vessel remains in the new heeled position without developing a righting moment or an upsetting moment to return it to the upright position. **Why the other options are incorrect:** * **A) The vessel possesses positive stability:** Positive stability occurs when $GM > 0$. This happens when $KM > KG$ (the metacenter M is above the center of gravity G). The vessel develops a righting moment and returns to the upright position. * **C) The vessel possesses negative stability:** Negative stability (or loll/unstable equilibrium) occurs when $GM < 0$. This happens when $KG > KM$ (the center of gravity G is above the metacenter M). The vessel develops an upsetting moment and will capsize or flop over to a large angle of inclination. * **D) The vessel possesses maximum stability:** Maximum stability is a qualitative term related to the maximum value of the righting arm or the range of stability, not a specific condition defined by $KG = KM$. Furthermore, zero stability ($GM=0$) is the threshold between stable and unstable conditions, making it the opposite of maximum stability.