Selina solutions concise physics class 9 icse Solutions for Chapter 5 chapter 5 upthrust in fluids archimedes principle and floatation

What do you understand by the term upthrust of a fluid? Describe an experiment to show its existence.

In what direction and at what point does the buoyant force on a body due to a liquid, act

What is meant by the term buoyancy

Define upthrust and state its S.I. unit

What is the cause of upthrust? At which point it can be considered to act?

Why is a force needed to keep a block of wood inside water?

A piece of wood if left under water, comes to the surface. Explain the reason

Describe an experiment to show that a body immersed in a liquid appears lighter than it really

is.

Will a body weigh more in the air or in vacuum when weighed with a spring balance? Give a reason for your answer

A metal solid cylinder tied to a thread is hanging from the hook of a spring balance. The cylinder is gradually immersed into water contained in a jar. What changes do you expect in the readings of spring balance? Explain your answer

A body dipped into a liquid experience an upthrust. State two factors on which upthrust on the body depends

How is the upthrust related to the volume of the body submerged in a liquid

A bunch of feathers and a stone of the same mass are released simultaneously in the air. Which will fall faster and why? How will your observation be different if they are released

simultaneously in a vacuum?

A body experiences an upthrust F1 in river water and F2 in seawater when dipped up to the same level. Which is more F1 or F2? Give reason

A small block of wood is held completely immersed in

(i) water,

(ii) glycerine, and then released. In each case, what do you observe? Explain the difference in your observation in the

two cases.

body of volume V and density ρ is kept completely immersed in a liquid of density ρL. If g id the acceleration due to gravity, write expressions for the following:

(i) The weight of the body

(ii) The upthrust on the body

(iii) The apparent weight of the body in liquid

(iv) The loss in weight of the body.

A body held completely immersed inside a liquid experiences two forces:

(i) F1, the force due to gravity, and

(ii) F2, the buoyant force. Draw a diagram showing the direction of these forces backing on the body and state the conditions when the body will float or sink.

Complete the following sentences:

(a) Two balls, one of iron and the other of aluminum experience the same upthrust when\ dipped completely in water if ________________

(b) An empty tin container with its mouth closed has an average density equal to that of a liquid. The container is taken 2m below the surface of that liquid and is left there. Then the container will ___________

(c) A piece of wood is held under water. The upthrust on it will be ___________ the weight of the wood piece

Prove that the loss in weight of a body when immersed wholly or partially in a liquid is equal to the buoyant force (or upthrust) and this loss is because of the difference in pressure exerted by the liquid on the upper and lower surfaces of the submerged part of the body

A sphere of iron and another of wood of the same radius are held underwater. Compare the, upthrust on the two spheres.

[Hint: Both have equal volume inside water.]

A sphere of iron and another of wood, both of the same radius are placed on the surface of the water.

State which of the two will sink? Give a reason for your answer

How does the density of material of a body determine whether it will float or sink in water

A body of density ρ is immersed in a liquid of density ρL. State condition when the body will

(i)float,

(ii) sink, in liquid.

It is easier to lift a heavy stone under water than in air. Explain

State Archimedes’ principle.

Describe an experiment to verify Archimedes’ principle.

A body will experience minimum upthrust when it is completely immersed in:

(a) Turpentine

(b) Water

(c) Glycerine

(d) Mercury

The S.I. unit of upthrust is:

(a) Pa

(b) N

(c) kg

(d) kg m-3

body of density ρ sinks in a liquid of density ρL. The densities ρ and ρL are related as:

(a) ρ = ρL

(b) ρ < ρL

(c) ρ > ρL

(d) nothing can be said

A body of volume 100cm3 weighs 5kgf in air. It is completely immersed in a liquid of

density 1.8 x 103 kg m-3, find: (i) the upthrust due to liquid and (ii) the weight of the body in liquid

A body weighs 450 gf in air and 310 gf when completely immersed in water. Find:

(i) The volume of the body,

(ii) The loss in weight of the body, and

(iii) The upthrust on the body.

State the assumption made in part (i).

You are provided with a hollow iron ball A of volume 15cm3 and mass 12g and a solid iron ball B of mass 12g. Both are placed on the surface of water contained in a large tub.

(a)

Find upthrust on each ball. (b) Which ball will sink? Give reason for your answer.(Density of iron = 8.0 gcm-3)

A solid of density 5000kgm-3 weighs 0.5kgf in air. It is completely immersed in water of density 1000 kg m-3. Calculate the apparent weight of the solid in water

Two spheres A and B, each of volume 100cm3 are placed on water (density =1.0g cm-3). The sphere A is made of wood of density 0.3g cm-3 and sphere B is made of iron of density 8.9g cm-3.

(a) Find: (i) the weight of each sphere, and (ii) the upthrust on each sphere.

(b) Which sphere will float? Give reason

The mass of a block made of a certain material is 13.5kg and its volume is 15 x 10-3 m3.

(a) Calculate upthrust on the block if it is held fully immersed in water

(b) Will the block float or sink in water when released? Give the reason for your answer

(c) What will be the upthrust on the block while floating? Take the density of water = 1000 kg m-3.

A piece of brass weighs 175gf in air and 150 gf when fully immersed in water. The density of water is 1.0gcm-3. (i) What is the volume of the brass piece? (ii) Why does the brass piece

weigh less in the water?

A metal cube of edge 5cm and density 9.0 gcm-3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 cm-3. Find the tension in the thread.

(Take g = 10 m/s2)

[Hint: Tension in thread = apparent weight of the cube in liquid

A block of wood is floating on water with its dimensions 50cm x 50 cm x 50 cm inside water.

Calculate the buoyant force acting on the block. Take g = 9.8N kg-1.

A block of mass 3.5kg displaces 1000cm3 of water when fully immersed inside it. Calculate:

(i) the volume of the body, (ii) the upthrust on the body, and (iii) the apparent weight of the body in water.

Define the term density

What are the units of density in (i) C.G.S. and (ii) S.I. system

Express the relationship between the C.G.S. and S.I. units of density

The density of iron is 7800 kg m-3. What do you understand by this statement

Write the density of water at 4℃ in S.I. unit

How are the (i) mass, (ii) volume, and (iii) density of a metallic piece affected, if at all, with increase in temperature?

Water is heated from 0℃ to 10℃. How does the density of water change with

temperature

Complete the following sentences:

(i) Mass = _________ x density

(ii) S.I. unit of density is ___________

(iii) Density of water is _______ kg m-3

(iv) Density in kg m-3 = ________ x density in g cm-3

What do you understand by the term relative density of a substance

What is the unit of relative density?

Differentiate between density and relative density of a substance?

With the use of Archimedes’ principle, state how you will find the relative density of a solid denser than water and insoluble in it. How will you modify your experiment if the solid is soluble in water?

A body weighs W gf in air and W1 gf when it is completely immersed in water. Find:

(I) volume of the body, (ii) upthrust on the body, (iii) relative density of the material of the body

Describe an experiment, using Archimedes’ principle, to find the relative density of a liquid.

A body weighs W1 gf in air and when immersed in a liquid it weighs W2 gf, while it weighs W3 gf on immersing it in water. Find: (i) volume of the body (ii) upthrust due to liquid (iii)

relative density of the solid and (iv)relative density of the liquid

The relative density of a substance is expressed by comparing the density of that substance with the density of:

(a) Air

(b) Mercury

(c) Water

(d) Iron

The unit of relative density is:

(a) g cm-3

(b) kg m-3

(c) m3 kg-1

(d) no unit

The density of water is:

(a) 1000 g cm-3

(b) 1 kg m-3

(c) 1 g cm-3

(d) None of these

The density of copper is 8.83 g cm-3. Express it in kg m-3.

The relative density of mercury is 13.6. State its density in (i) C.G.S. unit (ii) S.I. unit

The density of iron is 7.8 x 103 kg m-3. What is its relative density?

The relative density of silver is 10.8. Find its density

Calculate the mass of a body whose volume is 2m3 and relative density is 0.52

Calculate the mass of air in a room of dimensions 4.5m x 3.5m x 2.5m if the density of air at

N.T.P. is 1.3 kg m-3

A piece of stone of mass 113g sinks to the bottom in the water contained in a measuring cylinder and the water level in-cylinder rises from 30ml to 40ml. Calculate R.D. of stone

A body of volume 100cm3 weighs 1 kgf in air. Find: (i) its weight in water and (ii) its relative density.

A body of mass 70kg, when completely immersed in water, displaces 20,000 cm3 of water.

Find: (i) the weight of the body in water and (ii) the relative density of material of the body.

A solid weighs 120gf in air and 105 gf when it is completely immersed in water. Calculate

the relative density of solid.

A solid weighs 32 gf in air and 28.8 gf in water. Find: (i) the volume of solid, (ii) R.D. of solid, and (iii) the weight of solid in a liquid of density 0.9gcm-3.

A body weighs 20gf in air and 18 gf in water. Calculate relative density of the material of

the body

A solid weighs 1.5 kgf in air and 0.9kgf in a liquid of density 1.2 x 103 kg m-3. Calculate R.D. of solid.

jeweler claims that he makes ornament of pure gold of relative density 19.3. He sells a bangle weighing 25.25 gf to a person. The clever customer weighs the bangle when immersed in water and finds that it weighs 23.075 gf in water. With the help of suitable calculations find out whether the ornament is made of pure gold or not.

[Hint: Calculate R.D of the material of bangle which comes out to be 11.6

A piece of iron weighs 44.5 gf in air. If the density of iron is 8.9 x 103 kg m-3, find the weight of the iron piece when immersed in water.

A piece of stone of mass 15.1g is first immersed in a liquid and it weighs 10.9 gf. Then on immersing the piece of stone in water, it weighs 9.7 gf. Calculate:

(a) The weight of the piece of stone in the air,

(b) The volume of the piece of stone,

(c) The relative density of stone,

(d) The relative density of the liquid.

State the principle of floatation

A body is held immersed in a liquid. (i) Name the two forces acting on the body and draw a diagram to show these forces. (ii) State how do the magnitudes of two forces mentioned in part

(i) determine whether the body will float or sink in the liquid when it is released.

(iii) What is the net force on the body if it (a) sinks, (b) floats?

When a piece of wood is suspended from the hook of a spring balance, it reads 70 gf. The word is now lowered into the water. What reading do you expect on the scale of spring balance?

A solid iron ball of mass 500g is dropped in mercury contained in a beaker, (a) Will the ball float or sink? Give reason. (b) What will be the apparent weight of the ball? Give reason

How does the density ρS of a substance determine whether a solid piece of that substance

will float or sink in a given liquid of density ρL?

Explain why an iron nail floats on mercury, but it sinks in water.

[Hint: Density of iron is less than that of mercury but more than that of water]

A body floats in a liquid with a part of it submerged inside liquid. Is the weight of floating

body greater than, equal to or less than upthrust?

A homogenous block floats on water (a) partly immersed (b) completely immersed. In each

case state the position of centre of buoyancy B with respect to the centre of gravity G of the

block

The figure shows the same block of wood floating in three different liquids A, B, and C of densities ρ1, ρ2, and ρ3 respectively. Which of the liquid has the highest density? Give a reason for your answer

Draw a diagram to show the forces acting on a body floating in water with its some part submerged. Name the forces and show their points of application.

How is the weight of water displaced by the floating body related to the weight of the body itself?

What is center of buoyancy? State its position for a floating body with respect to the centre of gravity of the body.

A balloon filled with helium gas floats in a big closed jar which is connected to an

evacuating pump. What will be your observation, if air from the jar is pumped out? Explain your answer

A block of wood is so loaded that it just floats in the water at room temperature. What change will occur in the state of floatation, if

(a) Some salt is added to water,

(b) Water is heated

A body of volume V and density ρS floats with volume v inside a liquid of density ρL. Show that

\frac{v}{v}=\frac{\rho_{S}}{\rho_{L}}

Two identical pieces, one of ice (Density=900 kgm-3)and other of wood (density=300 kg m-3) float on water.

(a) Which of the two will have more volume submerged inside water?

(b) Which of the two will experience more upthrust due to water?

Why is floating ice less submerged in brine than in water

A man first swims in sea water and then in river water.

(i) Compare the weights of sea water and river water displaced by him.

(ii) Where does he find it easier to swim and why?

An iron nail sinks in water while an iron ship floats on water. Explain the reason

What can you say about the average density of a ship floating on water in relation to the density of water?

A piece of ice floating in a glass of water melts, but the level of water in the glass does not change. Give reason.

[Hint: Ice contracts on melting]

A buoy is held inside water contained in a vessel by tying it with a thread to the base of the vessel. Name the three forces that keep the buoy in equilibrium and state the direction in which each force acts.

A loaded cargo ship sails from sea water to river water. State and explain your observation

Explain the following:

(a) Icebergs floating in the sea are dangerous for ships.

(b) An egg sinks in freshwater but floats in a strong salt solution

(c) A toy balloon filled with hydrogen rises to the ceiling, but if filled with carbon dioxide sinks to the floor

(d) As a ship in the harbor is being unloaded, it slowly rises higher in water

(e) A balloon filled with hydrogen rises to a certain height and then stops rising further.

(f) A ship submerges more as it sails from seawater to river water

For a floating body, its weight W and upthrust FB on it are related as:

(a) W > FB

(b) W < FB

(c) W = FB

(d) Nothing can be said

A body of weight W is floating in a liquid. Its apparent weight will be:

(a) Equal to W

(b) Less than W

(c) Greater than W

(d) Zero

the body floats in a liquid A of density ρ1 with a part of it submerged inside liquid while in

liquid B of density ρ2 totally submerged inside the liquid. The densities ρ1 and ρ2 are related as:

(a) ρ1 = ρ2

(b) ρ1 < ρ2

(c) ρ1 > ρ2

(d) nothing can be said

A rubber ball floats on water with its 1/3rd volume outside water. What is the density of rubber

A block of wood of mass 24kg floats on water. The volume of wood is 0.032 m3. Find:

(a) The volume of the block below the surface of the water,

(b) The density of the wood.

(density of water = 1000 kg m-3)

A wooden cube of side 10cm has a mass 700g. What part of it remains above the water surface while floating vertically on the water surface?

A piece of wax floats on the brine. What fractions of its volume is immersed?

Density of wax = 0.95 g cm-3, density of brine = 1.1 gcm3

If the density of ice is 0.9 g cm-3, what portion of an iceberg will remain below the surface of the water in a sea? (Density of seawater = 1.1 g cm-3)

A piece of wood of uniform cross-section and height 15cm floats vertically with its height 10cm in water and 12cm in spirit. Find the density of (i) wood and (ii) spirit.

A wooden block floats in water with two-third of its volume submerged.

(a) Calculate the density of the wood.

(b) When the same block is placed on oil, three-quarter of its volume is immersed in oil. Calculate the density of oil.