Question 54

The Correct Answer is D. ### Explanation for D ("positive") When the height of the metacenter ($\text{GM}$) is greater than the height of the center of gravity ($\text{G}$), the ship (or floating body) has a positive metacentric height ($\text{GM} = \text{KM} - \text{KG} > 0$, where $\text{K}$ is the keel and $\text{M}$ is the metacenter). * A **positive metacentric height** signifies that the metacenter ($\text{M}$) is above the center of gravity ($\text{G}$). * When a ship heels, a righting moment is generated, tending to return the ship to its upright position. * This condition results in **stable equilibrium**, and this type of stability is universally termed **positive stability**. Therefore, when the equilibrium position is stable, the stability itself is positive. ### Explanation of Why Other Options Are Incorrect **A) neutral:** Neutral stability occurs when the metacenter ($\text{M}$) coincides exactly with the center of gravity ($\text{G}$), resulting in a metacentric height ($\text{GM}$) of zero. In this state, if the body is tilted, it remains in the new tilted position without returning or capsizing. This contradicts the premise that the equilibrium position is stable (which implies a righting moment). **B) unstable:** Unstable equilibrium occurs when the metacenter ($\text{M}$) is below the center of gravity ($\text{G}$), resulting in a negative metacentric height ($\text{GM} < 0$). In this state, any small tilt generates a capsizing moment. This contradicts the premise that the upright equilibrium position is stable. **C) negative:** Negative stability is the technical term used to describe the condition of unstable equilibrium (where $\text{M}$ is below $\text{G}$). Since the prompt states the equilibrium is stable, the stability cannot be negative.