🔍 Key Concepts

• Free surface effect (FSE) formula for reduction in GM: ( , , \text{Free Surface Correction} = \frac{\rho_{liquid}}{\rho_{sea}} \cdot \frac{I}{\Delta} , , ) where (I) is second moment of area of the free surface and (\Delta) is displacement • How to compute second moment of area for a rectangular tank free surface: ( I = \frac{b^3 l}{12} ) (be clear which dimension is which) • Effect of different specific gravities (SG) inside the tank and outside the ship on the free surface correction

💭 Think About

• Which tank dimensions represent the free surface plane (the surface of the water) and which dimension should not be used in the moment of inertia calculation? • How do you convert the given displacement in tons into consistent units that match the tank dimensions given in feet? • How does the fact that the tank liquid is fresh water while the vessel floats in saltwater change the basic free surface correction? Do you need to apply a density (SG) ratio?

✅ Before You Answer

• Be sure you are using the correct formula for the second moment of area of a rectangle about a horizontal axis through its centroid, matching the free surface plane dimensions. • Verify that all units are consistent: length in feet, displacement in long tons vs. weight in pounds, and that (g) cancels appropriately if you use weight instead of mass. • Before picking an answer, confirm whether you have applied the SG ratio (fresh vs. salt) correctly in the free surface correction; a missing or inverted ratio will push your result noticeably away from the correct choice.