JKBOSE 9th Class Science Solutions Chapter 5 Floatation

◆ Force acting perpendicular to the surface of an object is called thrust.

◆ Thrust acting per unit area is called pressure.

∴  Pressure =  Thrust / Area

◆ SI unit of pressure is N m^-2 (or N/m²) or pascal (Pa).

◆ Pressure exerted on an enclosed liquid is transmitted equally in all directions.

◆ All bodies when immersed in liquid experience an upward force called up thrust or Buoyant force.

◆ The value of Buoyant force depends upon the density of liquid.

◆ If the weight of an immersed body is more than the up thrust then the body sinks in the liquid.

◆ Those bodies float which have density less than the density of the liquid in which they are immersed.

◆ Those bodies, which have density more than the density of the liquid in which it is immersed sink.

◆ According to Archimedes’ principle when a solid body is completely or partially immersed in a liquid and of the weight of the body is equal to the weight of the liquid displaced by the immersed part of the body then the body floats.

◆ Relative density of a substance is defined as the ratio of density of the substance to density of same volume of water.

∴ Relative density = Density of substance / Density of water

Relative density has no unit.

◆ Archimedes principle states that when a solid body is wholly or partly immersed in a liquid then the body experiences an upward thrust due to liquid displaced by the immersed part of the body.

⇒ Thrust. The total force acting perpendicular to the surface of the body is called thrust.

⇒ Buoyant Force. The upward thrust applied by the liquid on the immersed body is called Buoyant force.

⇒ Pressure. Thrust acting per unit area of the surface in contact is called pressure.

⇒ Density. Mass per unit volume of the substance is called the density of the substance or it is termed as the ratio of mass of a body to its volume.

∴ Density = Mass of the body / Volume of the body

SI unit of density is kg/m³.

⇒ Relative Density. Relative density of a substance is defined as the ratio of density of the substance to the density of same volume of water. Since it is the w ratio of two similar quantities, therefore it is only a number. It is also called specific gravity of the substance.

⇒ Archimedes Principle. This principle states that whenever a solid body is immersed in a liquid either wholly or partly then it experiences an upward thrust due to the displaced liquid.

Ans.— We know force per unit area is called pressure i.e. P = F/A. Now for the constant force, the pressure experienced is inversely proportional to area. Now, when the string is thin, it has less area of cross-section and hence, exerts greater pressure on the hand for the given weight of school bag. Thus, it becomes difficult to hold the school bag.

Ans.— Buoyancy. It is an upward thrust acting in a body when the body is completely or partly immersed in a fluid (i.e. thrust get or a gas).

Ans.— When the object has density less than the density of water i.e. 1 gm/cm³ then it, floats on the surface of water, because, it displaces more weight of water than its own weight. The upward force applied by displaced water is called buoyant force. As buoyant force is more than its own weight, therefore, it floats.

When the object has density more than 1 gcm -³, then it sinks in water, because, it always displaces less weight of water than its own weight. As buoyant force is less than its own weight, therefore, it sinks.

Ans.— With weighing machine, we find weight and not mass, Your weight as noted by machine is 42 kg f (or 42 kg wt) and not 42 kg. The actual weight is more than 42 kg f, since you have displaced some air when weighed in it. However, mass will remain the same in all cases.

Ans.— The bag of cotton will actually be heavier than the iron bar. Cotton is bulky and has more area as compared to the area of iron bar. Due to more area occupied by cotton bag it experiences more up thrust because of displaced volume of air. This up thrust reduces the downward pull and hence its weight as recorded by the weighing machine will be lesser.

Ans.— If an object is immersed in a liquid then the buoyant force due to displaced liquid acts on the object in vertically upward direction.

Ans.— As density of plastic is less than the density of water. The upward thrust applied by displaced water on the plastic will be more than the weight of the plastic. So plastic block will float on water.

Sol.— Here, density of water, P_w = 1 gm cm -³

Mass of substance, m = 50 g

Volume of substance , V = 20 cm³

We know, density of substance, p = m/v

= 50 g/ 20 cm³ (1g cm -³)

= 2.5 g cm -³

As the density of the substance is greater than the density of water, the given substance

will sink in water.

Solution.—  Here, mass of the packet (m) = 500 g

Volume of packet (V) = 350 cm³

∴ Density of sealed packet p = m/v = 500 g/ 350 cm -³

= 1.43 g cm -³

But Density of water P_w = 1 g cm -³

As density of sealed packet is more than that of water, the sealed packet will sink in water.

∴ Volume of sealed packet immersed in water

= V = 350 cm³

Weight of water displaced by the packet

= V_pw

= 350 × 1

= 350 g Ans.

Ans.— Archimedes Principle. According to this principle when a solid body is immersed either completely or partially in a liquid, it experiences an upward thrust which is equal to the weight of the liquid displaced by the immersed part of the body.” the body.”

Experimental Verification. Take a stone piece and tie it to the hook of a spring balance. Hold the spring balance in your hand or support it from the stand so as to the stone piece as shown in fig.

Note, the reading on the spring balance to know the weight of the stone. Now pour some water a beaker with and slowly immerse the stone in the water while with the hook of spring balance as shown in fig. (b). You will see that spring balance shows a siging decreased reading i.e. weight of stone is decreased after it is immersed in the water. des Subtract the two readings to know the decrease in the weight of stone. As soon as the stone is immersed in the water it displaces water equal to its own volume. Collect this water in other beaker and measure its weight. You will find that this weight of water is equal to the decrease of weight of the stone. Thus Archimedes’ principle is proved.

(i) Archimedes’ principle is used in designing ships and submarines.

(ii) Lactometers are constructed on Archimedes’ Principle which are used to measure purity of a sample of milk.i

(iii) Hydrometers used to measure density of liquid are also based on Archimedes’ principle.

Ans.— Density of a substance is defined as the mass of a substance contained in a unit volume.

Density = Mass / Volume

Its SI unit is kg m-³

Relative density or specific gravity is the ratio of density of substance to the density of same volume of water

 R.D or S.G. = Density of substance/Density of water

Density of water is 1,000 kg m-³ in SI.

According to Archimedes’ principle, when a body is immersed in water, the loss of weight in water is equal to the weight of an equal volume of water. i.e., weight of water displaced. Hence R.D. can be written as

R.D. = Weight of substance / Loss of weight of body in water

Ans.— Buoyancy. When a body is immersed partially or wholly in a fluid (liquid or gas), it displaces fluid. The displaced fluid exerts an upward force on the body. The upward force acting on a body immersed in a fluid is called upthrust or force of buoyancy and the phenomenon is called buoyancy.

The buoyancy acts through the centre of gravity of the displaced fluid which is called centre of buoyancy.

Ans.— Archimedes’ Principle. When a solid body is immersed completely or partially in a fluid, it experiences an upward thrust which is equal to the weight of the fluid displaced by the immersed part of the body.

Ans.— (a) Buoyant force.

(b) An object will float water if its density is less than that of water. In this case the upthrust due to displaced water will be more than the weight of the object.

While the object will sink if its density is more than that of water. In this case up thrust due to displaced water will be less than the weight of the object.

Ans.— Two forces which act on a body immersed in a liquid are :

(i) Weight of the body acting downward.

(ii) An up thrust due to displaced liquid.

Ans.— To move submarine under water, water is pumped in its special tanks. This causes a net increase in weight and thus submarine goes down in water.

To bring the submarine upon the surface of sea, the water from the tanks is thrown out by pumps. When water from the tanks of submarine is taken out, the net weight of the submarine decreases without any change in its volume and it comes up on the surface of water.

Ans.— (i) Dams and big buildings have wide foundations for safety, because they may not collapse under high pressure of the building.

(ii) A pin sinks in water while it floats on honey, because honey has greater density so it produces more buoyant force.

Ans.— A steel needle sinks in water because it displaces less weight of water which provides less buoyant force than the actual weight of the needle. On the other hand, steel ship floats because it displaces a large weight of water which provides a greater buoyant force to keep it a float.

Ans.— (a) We know Pressure = Thurst / Area. For the given thrust, pressure ∝ 1 / Area. Thus the effect of the same magnitude of force is more when the area of surface in contact is less. Hence a sharp blade is more effective in cutting an object than a blunt blade.

(b) The density of the cork piece is less than the density of water, and the density of the iron piece is more than the density of water. Hence, the cork piece floats but the iron piece sinks in water.

Ans.— (a) Swimmers are provided with an inflated rubber jacket to increase the volume such that density is decreased, which is helpful for swimming.

(b) It is easier to swim in sea water than in river water because density of sea water is more than water of the needle sinks in a river while a ship float on it.

Ans.— (i) A body will sink in a liquid if its density is greater than the density of the liquid.

(ii) A body will float in a liquid if its density is less than the density of the liquid.

(iii) A body will be in equilibrium at any submerged depth if the density of the body equal to the density of the liquid.

Ans.— Buoyancy. Upward force experienced by an object when it is immersed in a fluid is called force of buoyancy.

Ans.— If the density of object is less than water, it will float.

Ans.— When density of the object is more than that of liquid.

Ans.— Because density of steel is more than the density of water but less than the density of mercury.

Ans.— The swimmer is exerted by an upward force by displaced water. This causes buoyancy and makes the swimmer feel light.

Ans.— So that pressure acting on the road due to weight of truck or motor-bus may be small.

Ans.—The army tank rests upon a continuous broad chain. So, the total surface area is large and pressure on road due to weight of tank is not very high.

Ans.— Gold is denser than mercury. [Density of gold is 19,300 kg m-3 and that of mercury 13,600 kg m-³]

Ans.— Relative density has no unit because it is a ratio of two terms having same units. So relative density is expressed in numbers only.

Ans.— Density of silver is 10,500 kg m -³ or 10.5 g cm -³.

(A) side way

(B) downward

(C) upwards

(D) cannot say.

(A) N

(B) N/m

(C) N m²

(D) N/m²

Ans.—(D) N/m²

(A) P = FA

(B) F = P/A

(C) P = F/A

(D) P = F/A²

Ans.— (C) P = F/A

(A) kg/m

(B) kg/m²

(C) kg/m³

(D) None

Ans.— (C) kg/m³

(A) relative density

(B) specific gravity

(C) density

(D) none of these

Ans.— (C) density

(A) 2 N

(B) 8 N

(C) 10 N

(D) 12 N

Ans.— (A) 2 N

(A) immediately sink

(B) first float and then sink

(C) not be easily drowned

(D) be weightless.

(A) weight of the body

(B) mass of the body

(C) loss of weight of the body

(D) apparent weight.

(A) maximum when length and breadth form the base

(B) maximum when breadth and width form the base

(C) maximum when width and length form the base

(D) the same in all the above three cases.

Ans.— (B) maximum when breadth and width form the base

(A) Pressure

(B) Volume

(C) Momentum

(D) Density

Ans.— (D) Density