🔍 Key Concepts

• Use the rolling period formula that relates beam (B), rolling period (T), and metacentric height (GM): it has the form (T = C \cdot \dfrac{B}{\sqrt{GM}}) with a constant C around 0.44–0.45 in still water. • Remember to solve the formula for GM (algebra) before plugging in the numbers so you don’t mix up the steps. • Think about the relationship between GM and rolling period: a small GM gives a slow, lazy roll (long period); a large GM gives a quick, snappy roll (short period).

💭 Think About

• First, rearrange the rolling period formula to make GM the subject. What does GM equal in terms of T, B, and the constant? • When you plug in B = 40 ft and T = 20 s, is GM going to be a small fraction of a foot or several feet? Compare that to the choices. • Check whether the result makes physical sense: does a 20‑second roll on a 40‑ft beam vessel suggest a very stiff (large GM) or tender (small GM) ship?

✅ Before You Answer

• Be sure you square the correct term when solving for GM: only one part of the expression gets squared when you isolate GM. • Use a realistic constant C ≈ 0.44–0.45 for this type of exam problem; don’t invent a new constant. • After computing GM, compare your number to the choices and pick the one closest to your calculated value (don’t forget to keep the answer in feet).