Let's break down the problem: **Given:** - Rectangular tank dimensions: 6 m (length), 4 m (width), 2 m (height) - Floating in a fluid of density ρ - The tank is placed with the 6 m length **vertical** - Depth of immersion = 4 m **Question:** The rectangular tank is in _______ equilibrium (Stable/Unstable/Neutral/None of these). --- ### **Analysis** When a floating body is in equilibrium, its stability depends on the **metacentric height (GM)**: - **Stable equilibrium:** GM > 0 (metacentre M is above the centre of gravity G) - **Unstable equilibrium:** GM < 0 (M is below G) - **Neutral equilibrium:** GM = 0 (M coincides with G) #### **Step 1: Orientation** - 6 m side is vertical → Height = 6 m - Cross-section in water: 4 m × 2 m #### **Step 2: Depth of immersion** - Immersion depth = 4 m (more than the tank's shorter height, which is 2 m) - This means the tank is submerged deeper than its smallest height, which is structurally odd, but let's proceed as per the data. #### **Step 3: Stability** For a floating body: - **Broader base (wider horizontally) → more stability** - **Narrow, tall base (vertical) → less stability** Here, the tank is standing **vertically** (6 m tall, narrow base of 4 m × 2 m). The depth of immersion (4 m) is large compared to the tank's width and height. #### **Physical Interpretation:** A tall and narrow floating object is generally **unstable**, as any slight tilt will cause it to topple over. --- ### **Conclusion** **The equilibrium is:** - **Unstable** **Correct option:** - **Unstable** --- If you need a detailed calculation of the metacentric height, let me know!