Stable Equilibrium of a Submerged Body

A completely submerged body can be stable, unstable or neutral. The stability of a submerged body depends on the positions of the center of buoyancy (B), center of gravity (G), and metacenter (M). The position of these points determines the stability of the body.

- Center of Buoyancy (B): It is the center of the displaced volume of water. The buoyant force acts through this point.

- Center of Gravity (G): It is the point through which the weight of the body acts. It is the point where the body is in balance.

- Metacenter (M): It is the point where the vertical line through the center of buoyancy (B) intersects the line through the center of gravity (G) when the body is slightly tilted.

Stable Equilibrium

A completely submerged body will be in stable equilibrium if the position of the center of buoyancy (B) is below the position of the center of gravity (G). This means that the weight of the body is below the buoyant force acting on the body. In this case, the body will tend to return to its original position after a small disturbance.

Explanation

When a completely submerged body is in stable equilibrium, its center of buoyancy (B) is below the center of gravity (G). This means that the buoyant force acting on the body is above its weight. The body is in a balanced state, and any small disturbance will cause the body to oscillate but eventually return to its original position.

If the body is tilted slightly, the center of buoyancy (B) will shift to a new position, and the metacenter (M) will be above the center of gravity (G). This will create a restoring moment that will return the body to its initial position.

Conclusion

In conclusion, a completely submerged body will be in stable equilibrium if the center of buoyancy (B) is below the center of gravity (G). This means that the weight of the body is below the buoyant force acting on the body. The body will tend to return to its original position after a small disturbance, making it stable.