Correct option is D
For a floating body to be in stable equilibrium, the position of the metacenter relative to the center of gravity plays a crucial role. Stability is achieved when the metacenter (M) is above the center of gravity (G) of the floating body. Here's why:
1.
Metacenter (M): This is the point where the buoyant force, acting vertically upwards, is considered to act when the body is slightly tilted. It is an important factor in determining the stability of a floating object.
2.
Center of Gravity (G): The center of gravity is the point where the total weight of the body is considered to act. It is usually denoted by 'G' and it pulls the body downward due to the force of gravity.
3.
Stable Equilibrium: When a floating body is disturbed (for example, tilted slightly), if the metacenter (M) is above the center of gravity (G), the buoyant force will generate a restoring moment that brings the body back to its original position, ensuring stability.
· In this situation, the line of action of the buoyant force shifts, but it passes through the metacenter (M), and the couple created between the buoyant force and the gravitational force acts to restore the body to its equilibrium position.
4.
Unstable Equilibrium: If the metacenter (M) is below the center of gravity (G), the restoring moment will act in the opposite direction, causing the body to tilt further, leading to instability.
5.
Neutral Equilibrium: If the metacenter coincides with the center of gravity, the body will neither return to its original position nor continue to tilt further. It will remain in its new tilted position.
