## 📖 Answer A > **A semisubmersible that repeatedly “flops” from port to starboard has a negative transverse metacentric height, which occurs when KMT is less than KGT, so choice A is correct.** --- ## 🔑 Key Facts |> • For transverse stability, the transverse metacentric height is \( GM_T = KMT - KGT \,\) where **KMT** is the transverse metacentric height above keel and **KGT** is the transverse center of gravity above keel. |> • If **KMT < KGT**, then \( GM_T < 0 \) (negative GM), meaning the vessel is **transversely unstable** and will flop from one side to the other instead of returning to upright. |> • A steady list to one side (not flopping) is usually caused by an **off‑center transverse center of gravity (TCG)**, not by negative GM. |> • Longitudinal properties (LCG, KML, etc.) mainly affect **trim** (bow‑stern attitude), not side‑to‑side list or flopping, which is governed by transverse stability. --- ## 🧭 Solution ::step 1:: |> A semisubmersible that **flops between port and starboard angles of list** does not settle at a stable angle. Instead, if you disturb it slightly, it rolls past upright and tends to “snap” over to the other side, then back again. This behavior indicates the vessel is **transversely unstable** at small angles — it has **negative transverse GM (GM_T < 0)**. ::step 2:: |> For transverse (side‑to‑side) stability, the key relationship is: |> |> \[ GM_T = KMT - KGT \] |> |> Where: |> - **KMT** = distance from Keel (K) to transverse Metacenter (M_T) |> - **KGT** = distance from Keel (K) to transverse center of Gravity (G_T) |> |> If: |> - \( KMT > KGT \Rightarrow GM_T > 0 \): **stable** – vessel tends to return to upright. |> - \( KMT = KGT \Rightarrow GM_T = 0 \): **neutral equilibrium** – vessel neither returns nor moves farther away. |> - \( KMT < KGT \Rightarrow GM_T < 0 \): **unstable** – vessel moves farther from upright (can flop from side to side). ::step 3:: |> Because the question describes a semisubmersible **flopping between port and starboard list**, we are clearly in the **unstable** case: \( GM_T < 0 \). |> |> Using the formula: |> \[ GM_T = KMT - KGT < 0 \Rightarrow KMT < KGT \] |> |> So the condition that matches this behavior is exactly **KMT less than KGT**, which is answer **A**. ::step Final Step:: |> Now we compare each other choice to what actually causes side‑to‑side flopping: |> - Flopping = **negative transverse GM (GM_T < 0)**. |> - Not just any list, not just trim, and not just off‑center weights — specifically **unstable small‑angle transverse stability**. --- ## ❌ Why Other Answers Are Wrong |> **Option B:** An off‑center **LCG** (Longitudinal Center of Gravity) affects **trim** (bow up/bow down), not side‑to‑side list. Flopping between port and starboard is a **transverse stability** problem, described by GM_T, not by LCG. |> **Option C:** \(KMT > KML\) compares **transverse** and **longitudinal** metacentric heights; their relative sizes do **not** determine whether the vessel is transversely stable near upright. Flopping is caused by **KMT being less than KGT** (negative GM_T), not by how KMT compares to KML. |> **Option D:** A large off‑center **TCG** relative to the level‑vessel TCB would produce a **steady list to one side**, where the vessel heels and stays there in a new equilibrium. It would not cause the vessel to flop back and forth; that flopping behavior requires **negative transverse GM (KMT < KGT)**, not just off‑center TCG. --- ## 💡 Takeaway > When a vessel flops from one side to the other instead of returning upright, it has **negative transverse GM**, which in K‑notation means **KMT is less than KGT**.