Submerged Body Stability – Relative Positions of Centers A fully submerged body is in stable equilibrium if its center of gravity lies below its center of buoyancy, so a small angular displacement produces a righting moment.

Introduction:
Stability of submerged bodies is governed by how the weight and buoyant force lines of action separate when the body is tilted. Understanding the roles of the center of gravity (G) and the center of buoyancy (B) is fundamental in naval architecture and underwater vehicle design.

Given Data / Assumptions:

• Rigid body completely submerged in a static liquid.
• Small angular displacements only (initial stability).
• Liquid is homogeneous and at rest.

Concept / Approach:

For a fully submerged body of fixed volume, the point about which the buoyant force effectively acts for small tilts is at B (the metacenter coincides with B, unlike surface-piercing bodies). When the body is disturbed, if G is below B, the restoring couple brings the body back (stable). If G is above B, the couple is overturning (unstable). If G coincides with B, the body is neutrally stable.

Step-by-Step Solution:

Verification / Alternative check:

Consider a dense sphere fully submerged: adding ballast to lower G increases stability because the lever arm for the restoring moment increases when G is beneath B.

Why Other Options Are Wrong:

Coincides with: Neutral, not stable. Lies above: Produces an overturning moment (unstable). Same vertical level as: Also neutral stability. Outside the fluid: Not applicable for a submerged body.

Common Pitfalls:

Confusing submerged bodies with floating bodies where the metacenter M differs from B; assuming stability depends on mass alone rather than geometry and G-B separation.

Final Answer:

lies below