Let's break down the problem: **Problem Statement:** - A rectangular tank: 6 m long, 4 m wide, 2 m high. - It is floating in a fluid of density ρ. - The tank is placed such that the 6 m length is vertical. - The depth of immersion is 4 m. - Asked: The equilibrium state of the tank (Neutral, Unstable, Stable, None). --- ### **Analysis** #### **Key Points:** - The tank's **height** is 2 m, but it is immersed to a **depth of 4 m** with its **6 m dimension vertical**. - This means the tank is vertical (6 m), width is 4 m, and "height" is now 2 m for the purposes of width in the water plane. #### **Equilibrium of Floating Body** - **Stable Equilibrium:** If the metacentric height (GM) is positive. - **Unstable Equilibrium:** If GM is negative. - **Neutral Equilibrium:** If GM is zero. #### **Depth of Immersion:** - The tank is only 6 m tall, so it can only be immersed up to 6 m. But the problem says it is immersed to a depth of 4 m, which is possible. #### **Key Observation:** - The tank's height is 2 m, but it is turned so its 6 m dimension is vertical. This means the tank is much "taller" than it is wide in the water, making it **top-heavy** if floating upright. #### **Stability:** - For stable equilibrium, the center of buoyancy should be below the center of gravity (for a floating body). - A tall, narrow floating body (like a stick standing on end in water) is **unstable** as it easily tips over. --- ### **Conclusion** **The rectangular tank is in _unstable_ equilibrium.** #### **Correct Answer:** - **Unstable** (Option 2) --- **Reason:** A tall, narrow floating object with a small base is prone to tipping over; thus, it is in unstable equilibrium when floating upright.