On a vessel of 10,000 tons displacement,...

Question 1 of 2707066636eec28f7522a1c51d095

On a vessel of 10,000 tons displacement, compute the reduction in metacentric height due to free surface in a hold having free water on tank tops. The hold is 50 feet long and 50 feet wide. What is the reduction in metacentric height?

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Question 1 of 27070

🔍 Key Concepts

• Free surface effect and its impact on metacentric height (GM) • Formula for free surface correction: moment of inertia of the free surface area divided by vessel displacement • Unit consistency: converting between square feet, tons, and feet

💭 Think About

• How do you calculate the second moment of area (moment of inertia) for a rectangular free surface (length × breadth)? • Once you have the free surface moment of inertia, how is it related to the reduction in GM for a given vessel displacement? • Are you keeping all units consistent (feet, tons, cubic feet of seawater) throughout your calculation?

✅ Before You Answer

• Confirm the correct formula for free surface correction: it involves the moment of inertia of the free surface divided by displacement. • Verify that you are using the dimensions of the free water surface (not the tank depth) when calculating the moment of inertia. • Double‑check that the final correction is expressed in feet of GM reduction, and that your numerical value matches one of the answer choices.