Question 65

The Correct Answer is B ### Explanation of why option B ("positive") is correct: The height of the metacenter ($KM$) and the height of the center of gravity ($KG$) determine the metacentric height ($GM$). The relationship is defined as $GM = KM - KG$. When the height of the metacenter ($KM$) is greater than the height of the center of gravity ($KG$), the resulting metacentric height ($GM$) is positive ($GM > 0$). A positive metacentric height indicates that the buoyant forces provide a righting moment, causing the body (such as a ship or a floating object) to return to its upright equilibrium position after a small angular disturbance. In the terminology of stability analysis, this condition is known as **positive stability**. ### Explanation of why the other options are incorrect: * **A) unstable:** The equilibrium is unstable only when the metacentric height is negative ($GM < 0$), which occurs when the height of the metacenter is *less* than the height of the center of gravity ($KM < KG$). * **C) neutral:** Neutral stability occurs when the metacenter coincides with the center of gravity ($KM = KG$), resulting in a metacentric height of zero ($GM = 0$). In this case, the body will remain at whatever angle it is disturbed to. * **D) negative:** Negative stability is the technical term used to describe the condition where the metacentric height is negative ($GM < 0$), which corresponds to an unstable equilibrium. Since the problem explicitly states the equilibrium position is *stable*, the stability cannot be negative.