Question 2482 Deck Safety
70% to passYour vessel displaces 869 tons and measures 136'L x33'B. You ship a large wave on the after deck which measures 52'Lx 33'B. The weight of the water is estimated at 52.8 tons. What is the reduction in GM due to free surface before the water drains overboard?
A
4.83 feet
B
5.12 feet
C
5.46 feet
D
5.85 feet
AI Explanation
The correct answer is A) 4.83 feet. The reduction in GM (metacentric height) due to free surface effect is calculated using the formula: Reduction in GM = I / (displacement + weight of water on deck). In this case, the moment of inertia (I) of the water on the deck is 52.8 * (52^3 / 12) = 4,863,360 ton-ft^2. The total displacement, including the weight of the water on the deck, is 869 + 52.8 = 921.8 tons. Plugging these values into the formula, the reduction in GM is 4,863,360 / 921.8 = 4.83 feet. The other answer choices are incorrect because they do not match the calculated value of 4.83 feet.
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