For a floating body to be in equilibrium

Solution(By Examveda Team)

A floating body is said to be in equilibrium when it remains stable and doesn't overturn or sink. This equilibrium is maintained by a combination of factors. The options provided outline these factors:

1. Meta center should be above e.g.: The metacenter (M) is a point above the center of buoyancy (B) in a floating body. When the metacenter is above the center of gravity (G), the body tends to return to its equilibrium position if disturbed. This stability is crucial for preventing overturning.
2. Center of buoyancy and e.g. must lie on the same vertical plane: The center of buoyancy (B) is the point where the buoyant force acts vertically upward. For equilibrium, the center of gravity (G) and center of buoyancy (B) must lie on the same vertical line. This ensures that the body doesn't tilt or rotate.
3. A righting couple should be formed: A righting couple is a moment that tends to restore a floating body to its original upright position when it is tilted. It is created by the displacement of water due to the tilt of the body. This righting couple counteracts any tendency for the body to capsize.
In summary, all of the provided options contribute to the conditions required for a floating body to be in equilibrium. The metacenter's position, alignment of centers of buoyancy and gravity, and the formation of a righting couple collectively ensure the stability and equilibrium of the floating body.