Explanation: Oscillation of a Floating Body

Introduction:
When a body is floating in a liquid, it experiences various forces such as buoyancy, gravity, and hydrostatic pressure. These forces determine the stability and motion of the body. When a small angular displacement is given to the body, it starts oscillating about a specific point. This point is known as the metacenter.

The Metacenter:
The metacenter is the point at which the vertical line passing through the center of buoyancy intersects the body's axis of rotation. It is a crucial point that determines the stability of the floating body. The metacenter is located above the center of gravity of the body.

Explanation:
When a floating body is given a small angular displacement, it creates a moment about the center of gravity. This moment causes the body to rotate. As the body rotates, the center of buoyancy also shifts due to changes in the submerged volume and shape of the body.

Stability:
The stability of the floating body depends on the relative positions of the center of gravity, center of buoyancy, and the metacenter. If the metacenter is above the center of gravity, the body is said to be stable. This is because any rotational displacement will create a moment that will tend to restore the body to its original position.

Role of the Metacenter:
The metacenter plays a crucial role in the oscillation of the floating body. When the body is displaced from its equilibrium position, a restoring moment is generated due to the shift in the center of buoyancy. This moment acts in the opposite direction to the displacement, causing the body to oscillate about the metacenter.

Effect of Metacenter's Position:
The position of the metacenter determines the nature of the oscillation. If the metacenter is above the center of gravity, the oscillation will be stable and the body will tend to return to its original position. However, if the metacenter is below the center of gravity, the oscillation will be unstable and the body will continue to rotate in the same direction, potentially capsizing.

Conclusion:
In conclusion, when a body floating in a liquid is given a small angular displacement, it starts oscillating about a point known as the metacenter. The metacenter is the point at which the vertical line passing through the center of buoyancy intersects the body's axis of rotation. The relative positions of the metacenter, center of gravity, and center of buoyancy determine the stability and oscillation of the floating body.