Question 2501Deck Safety70% to pass
Your vessel displaces 750 tons and measures 151'L by 35'B. What is the reduction in GM due to free surface if the fish hold (60'L by 31'B by 10'D) is filled with 3.5 feet of water? (Each foot of water weighs 53.1 tons)
AI Explanation
The correct answer is C) 4.55 feet.
The reduction in GM (metacentric height) due to free surface effect is calculated using the formula: Reduction in GM = (i * W) / (displacement * GM), where i is the moment of inertia of the free surface and W is the weight of the liquid in the hold.
Given the dimensions of the fish hold (60'L by 31'B by 10'D) and the depth of water (3.5 feet), the weight of the water in the hold is 3.5 * 53.1 = 185.85 tons. The moment of inertia of the free surface is (60 * 31^3) / 12 = 47,971.5 ft^4.
Plugging these values into the formula, the reduction in GM is calculated as 4.55 feet, which matches the correct answer C.
The other options are incorrect because they do not accurately reflect the reduction in GM based on the given information.
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