Conditions for Flotation in terms of density

CONDITIONS FOR FLOATATION IN TERM OF DENSITY: Factors Affecting Buoyant Force or Floatation :

The magnitude of buoyant force or floatation depends on the following factors:

(i) Density of the Fluid: The liquid having higher density exerts more upward buoyant force on an object than another liquid of lower density. This is the reason, why it is easier to swim in sea water in comparison to normal water. Because sea water has higher density and hence exerts a greater buoyant force on the swimmer than the fresh water having lower density.

(ii) Volume of Object Immersed in the Liquid: As the volume of solid object immersed inside the liquid increases, the upward buoyant force also increases.

The magnitude of buoyant force acting on a solid object does not depend on the nature of the solid object. It depends only on its volume. e.g. When two balls made of different metals having different weights but equal volume when fully immersed in a liquid, they will experience an equal upward buoyant force as both the balls displace equal weight of the liquid due to their equal volumes.

For bodies with no air space: An ice cube, wooden block, a rod, a nail, etc., are bodies that have no vacant space or air space,i.e. there is no air trapped in them. The condition for the floatation of such bodies and the liquid concerned.

Suppose the volume of abody is V and its density is $rho$ . Suppose it is immerged in a liquid of density $rho_{L}$ .

The mass of the body is M = $V_rho$

The weight of the body is W = Mg = V $rho$ g

The volume of the displaced liquid = V $rho_{L}$

The weight of this displaced liquid = V $rho_{L}$ g

Thus, the force of buoyancy B = V $rho_{L}$ g

The body will come up and float if

B > W

V $rho_{L}$ g = V $rho$ g

$rho_L> rho$

Thus, a body that has no air space will float only if its density is less than that of the liquid.

For bodies with air space: A small needle made of stainless steel sinks in water, but a larger bowl made up of stainless steel floats. This is beacause a bowl can displace a much greater volume of water than the volume of steel used to make it. A covered bowl which can hold one litre of milk, can displace slightly more than 1 litre of water when completely immerged in the water.So we should be more careful while using the equation.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The liquid having _______________ density exerts more upward buoyant force on an object than another liquid of lower density.
A. Lower	B. Higher	C. Less	D. None of these.
Right Option : B
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Question : 2

The liquid having higher density exerts __________________ upward buoyant force on an object than another liquid of lower density.
A. Less	B. more	C. Equal	D. None of these.
Right Option : B
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Question : 3

Which of the following are correct : (a) Sea water has higher density and hence exerts a greater buoyant force on the swimmer than the fresh water having lower density. (b) Fresh water has higher density and hence exerts a greater buoyant force on the swimmer than the sea water having lower density.
A. Only (a) is correct.		B. Only (b) is correct.
C. Both (a) and (b) are correct.		D. None of these
Right Option : A
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