For the stability of a floating body. The metacentre must be

Options

A. on the surface of the floating body
B. above the centre of gravity of the floating body
C. below the centre of gravity of the floating body
D. at the centre of gravity of the followig body

Answer

To determine the condition for the stability of a floating body, we need to analyze the relationship between the metacenter (M) and the center of gravity (G) of the body. Here’s a step-by-step solution:

### Step 1: Understand the Definitions
- **Floating Body**: A body that is partially submerged in a fluid, with some part above the fluid surface and some part below.
- **Center of Gravity (G)**: The point where the weight of the body acts vertically downwards.
- **Center of Buoyancy (B)**: The center of mass of the displaced fluid, which is the point of application of the buoyant force acting on the body.
- **Metacenter (M)**: The point where the vertical line through the center of buoyancy (B) intersects the original vertical line (geometric axis) when the body is tilted.

### Step 2: Analyze Stability Conditions
- When a floating body is tilted, the center of buoyancy (B) shifts due to the change in the submerged volume.
- The metacenter (M) is defined based on the new position of the center of buoyancy after tilting.

### Step 3: Establish the Conditions for Stability
- For a floating body to be in stable equilibrium:
- The metacenter (M) must be **above** the center of gravity (G).
- This configuration ensures that when the body is tilted, the buoyant force acts to restore the body to its original position.

### Step 4: Conclusion
- Therefore, for the stability of a floating body, the metacenter must be above the center of gravity.

### Summary
- **Stable Condition**: M > G (Metacenter above center of gravity)
- **Unstable Condition**: M < G (Metacenter below center of gravity)