🔍 Key Concepts

• Transverse shift of center of gravity (G) when lifting a weight with a boom off the centerline • Formula for GM (metacentric height) and how it relates to small-angle list: ( ,\tan(\theta) = \frac{GZ}{GM} ,) • How to compute the horizontal movement of G using the virtual work method: ( w \times d = \Delta \times GG_1 ,)

💭 Think About

• How does the lifted weight act on the ship once it is just clear of the deck: as part of the ship’s displacement or as an external load? • What is the horizontal lever arm of the weight relative to the ship’s original centerline, and how does that create a transverse shift in the ship’s center of gravity? • Once you find the new transverse position of G, how do you convert that off-center distance into an angle of list using GM and small-angle stability relationships?

✅ Before You Answer

• Be sure you are using the total displacement including the lifted weight when you relate ( w \times d ) to ( \Delta \times GG_1 ). • Confirm that you are working in consistent units (all distances in feet, all weights/forces in tons). • After finding ( \tan(\theta) ), double-check that the angle you compute is in degrees, not radians, before comparing to the multiple-choice options.