Understanding Floating Body Equilibrium

The stability of a floating body is determined by the relative positions of its centre of gravity (G) and a point called the metacentre (M).

The centre of gravity (G) is the point where the entire weight of the body is considered to act vertically downwards.

The metacentre (M) is the point of intersection of the line of action of the force of buoyancy when the body is tilted through a small angle, and the original vertical line passing through the centre of buoyancy (B) and the centre of gravity (G).

Conditions for Equilibrium

The type of equilibrium for a floating body depends on the position of the metacentre (M) relative to the centre of gravity (G). There are three main types of equilibrium:

• Stable Equilibrium: A body is in stable equilibrium if, when given a small displacement, it tends to return to its original position. This occurs when the metacentre (M) is located above the centre of gravity (G). The distance between M and G is called the metacentric height (GM), and for stable equilibrium, GM > 0.
• Neutral Equilibrium: A body is in neutral equilibrium if, when given a small displacement, it remains in the new position. This occurs when the metacentre (M) coincides with the centre of gravity (G). For neutral equilibrium, GM = 0.
• Unstable Equilibrium: A body is in unstable equilibrium if, when given a small displacement, it tends to move further away from its original position. This occurs when the metacentre (M) is located below the centre of gravity (G). For unstable equilibrium, GM < 0.

Analyzing the Given Condition

The question states that for a floating body, the metacentre is below the centre of gravity. Based on the conditions described above:

If the metacentre (M) is below the centre of gravity (G), the metacentric height (GM) is negative (GM < 0). This condition corresponds to unstable equilibrium.

In an unstable equilibrium, a small tilt will cause a restoring moment that acts to further increase the tilt, leading the body to capsize or move to a different orientation.

Conclusion

Therefore, for a floating body where the metacentre is below the centre of gravity, the body is said to be in unstable equilibrium.