Question

The metacentric height is the distance between the

• A. Centre of gravity of the floating body and the centre of buoyancy
• B. Centre of gravity of the floating body and the metacentre
• C. Metacentre and centre of buoyancy
• D. Original centre of buoyancy and new centre of buoyancy

Hint:

Remember the stability criterion for floating bodies: \[ GM>0 \Rightarrow \text{Stable} \] \[ GM=0 \Rightarrow \text{Neutral} \] \[ GM<0 \Rightarrow \text{Unstable} \]

Answer 1

The Correct Option is B

Concept: Metacentric height is an important parameter used to determine the stability of floating bodies. It is defined as the distance between the centre of gravity (\(G\)) and the metacentre (\(M\)). \[ \boxed{GM=\text{Metacentric Height}} \] where \[ G=\text{Centre of Gravity}, \] \[ M=\text{Metacentre}. \] A floating body is
• Stable if \(GM>0\)
• Neutral if \(GM=0\)
• Unstable if \(GM<0\)

Step 1: Understand the definition. When a floating body is given a small angular displacement, the centre of buoyancy shifts and the vertical line through the new centre of buoyancy intersects the original vertical axis at the metacentre. The distance between the centre of gravity and the metacentre is called the metacentric height.

Step 2: Identify the correct option. Hence, \[ \boxed{\text{Metacentric height is the distance between the centre of gravity and the metacentre}.} \] Therefore, the correct option is \[ \boxed{(B)\;\text{Centre of gravity of the floating body and the metacentre}.} \]