Understanding Floating Body Stability and the Metacentre

The stability of a floating body is a crucial concept in fluid mechanics, particularly important for designing ships, boats, and other floating structures. Stability refers to the ability of the body to return to its original position after being slightly disturbed or tilted.

Let's examine the factors presented in the options and determine which one primarily governs this stability:

• Material of the floating body: The material affects the body's density and distribution of weight, influencing the position of the centre of gravity. While important, it's not the direct governing factor for stability itself after the body is floating.
• Nature of the fluid: The nature of the fluid (specifically its density) determines the buoyant force acting on the body. A higher fluid density means a larger buoyant force for the same submerged volume. This affects how high or low the body floats, but the fluid's nature itself doesn't directly govern the stability once floating, provided the buoyant force is sufficient to balance the weight.
• Density of the body: Similar to the material, the overall density of the body determines the submerged depth required to balance the body's weight with the buoyant force. It influences the position of the centre of buoyancy, but it's not the primary factor determining whether the body returns to its equilibrium position after tilting.
• Metacentre of the floating body: The metacentre is a critical point used to determine the stability of a floating body. It is defined as the point of intersection of the line of action of the buoyant force when the body is tilted by a small angle with the vertical line passing through the original centre of buoyancy and centre of gravity. The position of the metacentre relative to the centre of gravity (specifically, whether it is above or below the centre of gravity) is the main determinant of the body's stability.

For a floating body, stability depends on the relative positions of three key points:

• Centre of Gravity (G): The point where the entire weight of the body is considered to act.
• Centre of Buoyancy (B): The centroid of the submerged volume of the body. The buoyant force acts vertically upward through this point.
• Metacentre (M): As described above, its position changes slightly with tilt, but for small angles, a fixed point M is considered.

The body is considered stable if the metacentre (M) is above the centre of gravity (G). The distance between M and G is called the metacentric height (GM), and a larger positive GM indicates greater stability.

Therefore, the primary factor governing the stability of a floating body is the position of the metacentre relative to the centre of gravity.