Stability of Floating Bodies

By Mallesham Devasane|Updated : July 18th, 2025

Stability of Submerged Body: It is classified into the three groups.

  • Stable Equilibrium: When centre of buoyancy lies above the centre of gravity, submerged body is stable.

04-Stability-of-floating-bodies (1)

  • Unstable Equilibrium: When B lies below G, then body is in unstable equilibrium.

04-Stability-of-floating-bodies (2)

  • Neutral Equilibrium: When B and G coincide then, body is in neutral equilibrium.

04-Stability-of-floating-bodies (3)

Stability of Floating Bodies: When the body undergoes an angular displacement about a horizontal axis, the shape of the immersed volume changes and so the centre of buoyancy moves relative to the body.
  • Stale Equilibrium: When a body is given a small angular displacement by external means and if body comes to its original position due to internal forces then, it is called stable equilibrium.

04-Stability-of-floating-bodies (4)

It occurs, when metacentre lies above centre of gravity.

  • Unstable Equilibrium: In the above case, if body does not come in its original position and moves further away then, it is known as unstable equilibrium. M lies below centre of gravity.

04-Stability-of-floating-bodies (5)

  • Neutral equilibrium: When a body is given a small angular displacement and it sets on new position then, body is called in neutral equilibrium. In this, M and G coincide.
04-Stability-of-floating-bodies (6)

Relation between B,G and M is GM 04-Stability-of-floating-bodies (1)

Here, l = Least moment of inertia of plane of body at water surface

G = Centre of gravity

B = Centre of buoyancy

M = Metacentre

04-Stability-of-floating-bodies (7)

04-Stability-of-floating-bodies (2)

V is volume submerged inside the water can be given as

04-Stability-of-floating-bodies (3)

Where b,d and x are the length, width and depth of the section or body.

04-Stability-of-floating-bodies (9)

BG is distance between centre of gravity and centre of buoyancy. (In other words, BG=distance between centre of gravity of whole body and centre of gravity of submerged part of body) When we find out GM then, we can determine the status of body as GM > 0 (stable equilibrium), GM < 0 (unstable equilibrium), GM = 0 (neutral equilibrium).

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Mallesham DevasaneMallesham DevasaneMember since Oct 2015
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Karthik Veeramani
Sir, in this topic Iyy formula is correct?
ravi

raviDec 6, 2016

Good information

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