Conditions Of Equilibrium Of Floating And Submerged Bodies

A floating or submerged body is said to be stable if it comes back to its original position after giving a slight disturbance. The condition of stability of these bodies depends on the position of its metacentre, centre of buoyancy and centre of gravity. The relationship between these points and the stability of body is described below.

Conditions of Stability of floating body

Stable equilibrium: M above G. if the metacentre is above the centre of gravity then the floating body is in stable equilibrium. From fig shown above when a body is given a slight tilt in clockward direction, the centre of buoyancy B will shift to new position B₁. The weight W of body acting downward through the centre of gravity G and the force of buoyancy F_B act vertically upward through centre of buoyancy B₁. The vertical line through the B₁ will cut the normal passing through the centre of gravity at metacentre M. Here the metacentre M is above the centre of gravity G. The couple formed by buoyant force F_B and the weight w of body tends the body rotate anti-clockwise and then the force couple bring back body to its original position.

Unstable equilibrium: M below G. when the body is given a slight tilt in a clockwise direction. If the metacentre M is below the centre of gravity G, then the couple formed by buoyancy F_B and weight W of body tends the body to tilt clockwise direction and thus the body will overturn.

Neutral equilibrium: M coincide G. If the metacentre is at the centre of gravity, then the torque formed by F_B and W is zero. In this condition, body said to be in neutral equilibrium.

Conditions of stability of Submerged body

For a submerged body the weight of body is equal to the buoyant force, W=F_B, and body has no tendency to move upward or downward. For example, a balloon submerged in the air.

Stable equilibrium: B above G. If the centre of buoyancy B is above the centre of gravity, the slight clockwise tilt produce a couple of force F_B and W in opposite direction. The body will return to its original position.

Unstable equilibrium: B below G. if the body is given a slight tilt, the couple of forces W and F_B also in the same direction.

Neutral equilibrium: B coincide G. There is no torque couple formed by W and F_B.