A cargo of 100 tons is to be loaded on deck 20 feet from the ship's centerline. The ship's displacement including the 100 tons of cargo will be 10,000 tons and the GM two feet. What would be the list of the vessel after loading the cargo?
• Transverse metacentric height (GM) and its role in small-angle stability and list • Formula for transverse shift of center of gravity due to an off-center weight: GG₁ = (w × d) / Δ • Relationship between tangent of the angle of list (tan θ), the transverse shift of G, and GM for small angles
• First, calculate how far the ship’s center of gravity moves sideways when 100 tons are placed 20 feet off the centerline on a 10,000‑ton displacement ship. What formula relates these three values? • Once you know the sideways shift of G, how can you relate this shift to GM to find the tangent of the list angle? Which small-angle stability formula connects these? • After you find tan θ, how do you convert that to degrees, and which of the answer choices is closest to that angle?
• Be sure you’re using displacement including the new cargo (10,000 tons), not excluding it, in your GG₁ calculation. • Check that you’re using feet consistently for distances and that weight units (tons) cancel correctly in the GG₁ formula. • Confirm that you use tan θ = (GG₁ / GM) (for small angles of list) before converting θ from radians (or using a calculator) to degrees to compare with the choices.
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