Stable Equilibrium in a Floating Body

A floating body is said to be in stable equilibrium when it returns to its original position after being displaced. In this state, the body is balanced and has a tendency to remain in the same position. To achieve stable equilibrium, certain conditions need to be met.

Centre of Gravity (CG) and Centre of Buoyancy (CB)

The center of gravity (CG) of an object is the point at which its entire weight can be considered to act. It is the average position of the weight distribution within the body. On the other hand, the center of buoyancy (CB) is the center of the volume of the fluid displaced by the body. It represents the point through which the buoyant force acts.

Metacentric Height (GM)

The metacentric height (GM) is a crucial factor in determining the stability of a floating body. It is the distance between the center of gravity (CG) and the metacenter (M). The metacenter is a theoretical point where the vertical line passing through the center of buoyancy (CB) intersects with the line of action of the weight of the body.

Explanation of Options

a) Its centre of gravity is below the centre of buoyancy:
This statement is not sufficient to determine stable equilibrium. The relative positions of CG and CB are important, but the metacentric height (GM) also plays a crucial role.

b) Its metacentric height is a positive value:
This statement is correct. When the metacentric height (GM) is positive, it indicates that the metacenter (M) is above the center of gravity (CG). This configuration ensures stable equilibrium because any disturbance causes the body to rotate and return to its original position.

c) Its metacentric height is zero:
When the metacentric height is zero, the metacenter (M) coincides with the center of gravity (CG). In this situation, the body becomes neutrally stable. Any disturbance will not cause the body to rotate, and it will remain in its new position.

d) Its metacentric height is a negative value:
When the metacentric height (GM) is negative, it indicates that the metacenter (M) is below the center of gravity (CG). This configuration leads to unstable equilibrium. Even a small disturbance can cause the body to capsize or overturn.

Therefore, the correct option for a floating body to be in stable equilibrium is when its metacentric height (GM) is a positive value.