Unstable Equilibrium and the Metacentre

In fluid mechanics, the concept of equilibrium plays a crucial role in understanding the stability of floating bodies. When a body is in equilibrium, it means that the forces acting on it are balanced, resulting in no net force or moment. However, the stability of a floating body depends on the position of its center of gravity (CG) relative to the metacentre (M).

Understanding the Metacentre

The metacentre is a virtual point in a floating body that represents the intersection of the vertical line passing through the center of buoyancy (B) and the normal line from the initial center of gravity (CG). It is important to note that the metacentre is a fixed point that remains the same, regardless of the body's inclination.

Stability of a Floating Body

The stability of a floating body is determined by the relative positions of the metacentre and the center of gravity. There are three possible scenarios:

1. Stable Equilibrium: If the metacentre (M) is above the center of gravity (CG), the body is in stable equilibrium. In this case, if the body is slightly tilted, a restoring moment is created that brings it back to its original position.

2. Neutral Equilibrium: If the metacentre (M) coincides with the center of gravity (CG), the body is in neutral equilibrium. In this case, the body will remain in any tilted position, as there is no restoring moment.

3. Unstable Equilibrium: If the metacentre (M) is below the center of gravity (CG), the body is in unstable equilibrium. This means that any slight disturbance will cause the body to overturn and not return to its original position.

Correct Answer and Explanation

The correct answer to the given question is option 'B': True. When the metacentre is below the center of gravity, the floating body is in unstable equilibrium. This is because the center of gravity acts as a pivot point, and any disturbance causes the body to overturn instead of returning to its original position.

In conclusion, the stability of a floating body is determined by the position of its center of gravity relative to the metacentre. If the metacentre is below the center of gravity, the body is in unstable equilibrium, and any disturbance will cause it to overturn.