Stable Equilibrium of a Submerged Body

To understand why the correct answer is option 'A', let's first define the terms involved:

1. Centre of Gravity (CG): It is the point through which the total weight of an object can be considered to act. It is the point where the entire weight of the object is concentrated.

2. Centre of Buoyancy (CB): It is the point at which the buoyant force, or the upward force exerted on a submerged object by the surrounding fluid, can be considered to act. It is the point where the entire buoyant force is concentrated.

Now, let's discuss the equilibrium conditions for a submerged body:

- When a body is fully or partially submerged in a fluid, it experiences an upward force called the buoyant force. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the body.

- For a body to be in equilibrium, the forces acting on it must be balanced. In the case of a submerged body, this means that the weight of the body and the buoyant force must be equal in magnitude and opposite in direction.

Why is Option 'A' Correct?

The correct answer is option 'A' because a submerged body will be in stable equilibrium when the centre of gravity is below the centre of buoyancy. Here's why:

- When the centre of gravity is below the centre of buoyancy, the body tends to return to its original position if it is slightly displaced.

- If the body is tilted or displaced from its equilibrium position, the centre of gravity and the centre of buoyancy will no longer be aligned vertically. As a result, a torque or turning moment is produced.

- This torque will cause a restoring force that acts to bring the body back to its original position. The body will oscillate back and forth around its equilibrium position until it comes to rest.

- This stable equilibrium occurs because the weight of the body acts downwards from the centre of gravity, while the buoyant force acts upwards from the centre of buoyancy. The weight and the buoyant force create a couple that tends to restore the body to its original position.

Therefore, option 'A' is the correct answer for a submerged body to be in stable equilibrium.