# Floating, Immersed body,Buoyant force

Archimedes’ Principle: body immersed in a fluid experiences a buoyant force equal to weight of fluid it displaces.

 B

Which body is heavier? A or B

Which fluid is denser? A or B

Buoyant force FB

FB = weight of displaced fluid

= g x (submerged volume of body)

HYDROMETER:

Instrument used to measure S.G of a fluid is based on principle of buoyancy

• Which fluid is more dense?

#### STABILITY

What is stability?

A body subjected to small angular displacement will try to get back to original.

Or, moments that try to rotate body get it back to where it was before.

·      Two moments try to restore body.

·      FBxa and Wxa

·      Lesser of the two is called “Righting Moment”

Righting moment = Wxa  , if W<FB

=  FB xa, if W>FB

CRITERION FOR STABILITY OF A FULLY SUBMERGED BODY IS THAT CENTER OF BUOYANCY MUST BE ABOVE CENTER OF GRAVITY.

#### FLOATING BODY: W<FB

·      Body will rise until W=FB

·      At equilibrium, W and FB are equal and opposite and lie in the same vertical line

·      Recall, for a fully submerged body center of buoyancy (B)and center of gravity (G)are fixed and the criterion for stability is that B is above G

·      For a floating body, B can move relative to G, depending on how much fluid is displaced.

·      Stability of floating body depends on its shape.