In order that a floating object be in a stable equilibrium its centre of buoyancy should be

Options

A. vertical below its centre of gravity
B. horizontally inline with its centre of gravity
C. vertically above its centre of gravity
D. may be anywhere

Answer

To determine the position of the center of buoyancy for a floating object to be in stable equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Floating Objects**: A floating object is in equilibrium when the buoyant force acting on it equals the weight of the object. The center of buoyancy is the point where the buoyant force can be considered to act.

2. **Defining Equilibrium**: For an object to be in stable equilibrium, it must satisfy both translational and rotational equilibrium. This means that the net force and net torque acting on the object must be zero.

3. **Identifying Forces**: When the object is floating, the weight (mg) acts downward through the center of gravity (G), and the buoyant force acts upward through the center of buoyancy (B).

4. **Torque Consideration**: If the object is tilted, the position of the center of buoyancy relative to the center of gravity determines whether the object will return to its original position (stable equilibrium) or continue to tilt (unstable equilibrium).

5. **Stable Equilibrium Condition**: For stable equilibrium, the center of buoyancy must be located above the center of gravity. This ensures that when the object is tilted, the buoyant force creates a restoring torque that brings the object back to its upright position.

6. **Conclusion**: Therefore, in order for a floating object to be in stable equilibrium, the center of buoyancy should be **vertically above the center of gravity**.

### Final Answer:
The center of buoyancy should be **vertically above the center of gravity** for a floating object to be in stable equilibrium.

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