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# Section B

## BUOYANCY & STABILITY OF

IMMERSED AND FLOATING BODIES

ARCHIMRDES PRINCIPLE
Whenever a body immersed wholly or partially in a liquid

## it is acted upon by a vertical upward liquid thrust equal to

the weight of the liquid displaced.

BUOYANCY
It is an upward thrust exerted by a liquid on a body floating
or immersed in it.It is equal to the weight of the liquid
displaced by the body.

CENTRE OF BUOYANCY

It

## is the point at which the buoyancy or upward liquid

thrust acts. The centre of buoyancy will be the centre of
gravity of the fluid displaced.

## Depth of immersion: h=bH/

STABILITY :
The stability of a body

can be determined by
considering what happens
when it is displaced from
its equilibrium.

## STABILITY OF IMMERSED BODIES

When a body is completely immersed in a liquid , its stability

## depends on the relative positions of the centre of gravity of the

body and the centroid of the displaced volume of fluid, which is
called the centre of buoyancy.
The position of Centre of gravity and Centre of buoyancy in case of
a completely sub-merged are fixed.
CONDITIONS OF EQUILIBRIUM OF IMMERSED BODIES
STABLE EQUILIBRIUM
UNSTABLE EQUILIBRIUM
NEUTRAL EQUILIBRIUM

## Lets take an example of a balloon which is completely

submerged in air

Where
FB = buoyant force.
W = weight of balloon.
G = centre of gravity.
B = centre of buoyancy.

STABLE EQUILIBRIUM

## When W=FB and point B is above G , the body

is said to be in stable equilibrium.

## If the balloon is given an angular displacement

in the clockwise direction, then W and FB
constitute a couple acting in the anti-clockwise
direction and brings the balloon in the original
position

UNSTABLE EQUILIBRIUM
If W=FB ,but B is below G,the body is in

unstable equilibrium.
A slight displacement to the body in the
clockwise direction, gives the couple due to
W and FB ,also in the clockwise
its original position .

NEUTRAL EQUILIBRIUM
If W=FB and B and G are at the same point ,the body is
said to be in Neutral Equilibrium
ANOTHER Figure is shown below for all three conditions.

## STABILITY OF FLOATING BODIES

The stability of a floating body is determined from the position

## of Meta centre(M).In case of floating body ,the weight of

body is equal to the weight of the liquid displaced.
The centre of buoyancy may take different positions w.r.t
centre of gravity, depending on the shape of the body and the
position in which it is floating.

## CONDITIONS OF EQUILIBRIUM OF FLOATING BODIES

STABLE EQUILIBRIUM
UNSTABLE EQUILIBRIUM
NEUTRAL EQUILIBRIUM

STABLE EQUILIBRIUM
If the point M is above G,the floating body will be in

stable equilibrium.
Centre of Buoyancy will shift from B to B1, Such that the
vertical line through B1, cuts at M.
Then the buoyant force FB through B1,and weight W
through G constitute a couple acting in the anticlockwise
direction and thus bringing the floating body in the
original position.

UNSTABLE EQUILIBRIUM
If point M is below G,the floating body will be in unstable

equilibrium
The disturbing couple is acting in the clockwise direction.
The couple due to buoyant force FB and W is also acting

## in the clockwise direction and thus overturning the body.

NEUTRAL EQUILIBRIUM
If the point M is at the centre of gravity of the body ,the
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