Question 2479Deck Safety70% to pass
Your vessel displaces 368 tons and measures 96'L x 28'B. You ship a large wave on the after deck. What is the reduction to GM due to free surface before the water drains overboard, if the after deck measures 42'L x 28'B and the weight of the water is 36 tons?
AI Explanation
The correct answer is C) 5.43 feet.
The reduction in GM (metacentric height) due to free surface effect is calculated using the formula: Reduction in GM = (I/V) * W/Δ, where I is the moment of inertia of the free surface, V is the vessel's volume, W is the weight of the free surface, and Δ is the vessel's displacement.
In this case, the moment of inertia of the free surface (I) is calculated as (42'L x 28'B^3)/12 = 82,944 ft^4. With a vessel displacement of 368 tons and a free surface weight of 36 tons, the reduction in GM is calculated as (82,944 ft^4/368 ft^3) * (36 tons/368 tons) = 5.43 feet, which matches the correct answer choice C.
The other answer choices are incorrect because they do not accurately reflect the reduction in GM based on the given information.
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