Numericals On Upthrust In Fluids, Archimedes Principle and Floatation Class 9 ICSE Concise Physics

#Upthrust #ArchimedesPrinciple
BUOYANT FORCE:
When a body is immersed partially or wholly in a fluid it experiences an upward force is called UPTHRUST or BUOYANT FORCE.

WHEN ANY OBJECT IS IMMERSED IN A FLUID (LIQUIDS OR GASES) ,TWO FORCES ACT ON IT:
 its weight (force of gravity acting on a given mass) W which pulls it downwards through centre of gravity (G).
 Upthrust FB which the fluid exerts on the object pushing the object upwards through centre of buoyancy (B).


BUOYAN FORCE DEPENDS:

(1) Volume of the body immersed
(2)Density of the liquid
(3) Acceleration due to gravity

BUOYANCY:

The property of the liquid to exert upward force when immersed in a liquid is called Buoyancy.

DEPENDING ON THE DIRECTION OF THE RESULTANT FORCE , THE OBJECT WILL EITHER FLOAT OR SINK IN A FLUID:
I) Condition for sinking:
If W is greater than FB
i.e W – FB is the net force acting vertically downwards Density of solid ρs is greater than Density of solid ρL

1I) Condition for floating:
A) When a body is below the surface of the fluid but does not sink but rather floats:
If W = FB
i.e FB - W = 0 the net force is zero Density of solid ρs = Density of solid ρL

B) When body is floats, with only some part of it inside
If W is less thanFB
i.e FB - W is the net force acting vertically Upwards Density of solid ρs is less than Density of solid ρL
1) Reason for upthrust:

 When an object is immersed in a fluid it experiences pressure or force on its surface area at all points and in all directions.
 Pressure exerted by the fluid is same in all directions. (upwards, sideways or downward directions)
 Lateral pressure or force F on the sides of the walls of body are equal
and in opposite direction, hence they cancel each other or get neutralized.
 The pressure (P1) on the upper surface of the body in downward direction is less than the pressure ( P 2 )exerted on the lower surface in upward direction, due to difference in depth or height from free surface.
 Thus the difference in pressure P (in upward direction) = P 2 - P1
 Upthrust = (P 2 - P1)A ( in upward direction)


MATHEMATICAL EXPRESSION FOR UPTHRUST:
• Consider a cylindrical body PQRS of cross-sectional area AS immersed in a liquid of density ρL. The upper surface PQ is at a depth of h1 while its lower surface RS is at a depth h2 from free surface. Pressure on upper surface PQ is P1 = h1 ρL g 1
Pressure on lower surface SR is P2 = h2 ρL g 2
Difference in pressure is P2 - P1 = h2 ρL g - h1 ρL g = (h2 - h1 )ρL g Thrust = pressure x Area
 Resultant upward thrust / upthrust = (h2 - h1 )ρL g x AS = hS ρL g x AS [ ∵ (h2 - h1 ) = height of solid hS] Upthrust ( F B) = VS ρL g [∵ hS x AS = VS volume of solid]