🔍 Key Concepts

• Free surface effect and how it reduces GM (metacentric height) • How to compute moment of inertia of a rectangular tank about its centerline: I = (l × b³) / 12 • Relationship between free surface moment, displacement, and reduction in GM

💭 Think About

• First find the volume and then the total weight of water in the fish hold using the given depth and tons-per-foot value. How does this help you compare to the ship’s displacement? • Think about whether the reduction in GM depends on the actual weight of water in the tank, or on the geometry (length and breadth) of the free surface. • After finding the free surface moment (FSM) from the tank dimensions, how do you convert that FSM into a reduction in GM using the ship’s displacement (in tons)?

✅ Before You Answer

• Be sure you are using breadth of the free surface in feet, not the ship’s breadth, when computing the moment of inertia of the water surface. • Confirm that displacement is in tons and distances are in feet, so your GM reduction ends up in feet. • Check that you apply the formula in the correct order: find I for the tank’s free surface, then FSM, then divide by dispacement to get ΔGM.