The GZ curve for a stable ship is shown in the figure, where \( P \) is a point of inflection on the curve. Match the labels in Column 1 with the corresponding descriptions in Column 2.
The GZ curve for a stable ship is shown in the figure, where \( P \) is a point of inflection on the curve. Match the labels in Column 1 with the corresponding descriptions in Column 2.
Show Hint
1. The point \( R \) indicates the loss of stability, which is crucial for safety limits.
2. Maximum GZ value at \( Q \) represents the ship's maximum righting moment.
3. The slope at the origin (\( ST \)) relates to the initial stability.
4. Deck edge immersion point (\( P \)) is vital for assessing freeboard requirements.
- \( R - I; Q - II; ST - III; P - IV \)
- \( P - I; Q - II; ST - III; R - IV \)
- \( ST - I; Q - II; R - III; P - IV \)
- \( R - I; Q - II; P - III; ST - IV \)
The Correct Option is A
Solution and Explanation
Step 1: Understanding the GZ curve. The GZ curve (righting lever curve) represents the stability characteristics of a ship. The key points and segments of the curve provide significant insights into the ship's stability behavior: \( R \): The point of vanishing stability where the righting moment becomes zero. This corresponds to the angle of vanishing stability. \( Q \): The point where the GZ value is maximum, corresponding to the maximum righting lever. \( ST \): The slope of the curve at the origin represents the initial GM (metacentric height), which is a measure of the ship's initial stability. \( P \): The point of inflection where deck edge immersion occurs, indicating the angle at which the deck begins to submerge.
Step 2: Matching the columns. - \( R \): Angle of vanishing stability \( (I) \). - \( Q \): Maximum GZ \( (II) \). - \( ST \): Initial GM \( (III) \). - \( P \): Deck edge immersion \( (IV) \).
Conclusion: The correct matching is \( R - I; Q - II; ST - III; P - IV \), corresponding to option \( \mathbf{(A)} \).
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