Q1: A freely floating object is stable, if its centre of buoyancy

ANS:A - coincides with its centre of gravity.

A freely floating object is stable if its center of buoyancy lies below its center of gravity. Here's an explanation:

1. Center of Buoyancy: This is the center of the volume of water displaced by the floating object. It acts in the upward direction and is the point at which the buoyant force is considered to act.
2. Center of Gravity: This is the point where the force of gravity can be considered to act. It represents the average location of the mass of the object.
3. Stability: In a stable equilibrium, the center of gravity of the object must be located above the center of buoyancy. This ensures that when the object is tilted or disturbed, the buoyant force will act to restore it to its original position. If the center of gravity is above the center of buoyancy, the object will tend to return to its equilibrium position when disturbed.
4. Metacentre: The metacentre is a point in a floating body where the buoyant force, when the body is tilted slightly, appears to act. The stability of an object depends on the relationship between the center of gravity, the center of buoyancy, and the metacentre. However, the metacentre itself is not directly involved in determining the stability of a freely floating object.