Upthrust, Archimedes’ Principle and Floatation
Explore buoyancy, apparent weight, density, relative density and the principle of floatation through clear notes, interactive calculators and a complete solved exercise bank.
What is upthrust?
Upthrust, or buoyant force, is the upward force exerted by a fluid on an immersed body. It acts through the centre of buoyancy.
Archimedes’ principle
The upthrust on an immersed body equals the weight of the fluid displaced by the submerged part of the body.
Float or sink?
A body floats when its average density is less than or equal to the fluid density. It sinks when its density is greater.
Sink: ρbody > ρfluid
Formula toolbox
Density
S.I. unit: kg m−3
Apparent weight
Relative density of solid
Relative density of liquid
Floating fraction
Unit conversion
Buoyant-force calculator
Float-or-sink checker
Exercise 5(A) — Multiple Choice Type
13 solved questions
Question 1If an empty can is pushed into water, we feel :
Question
If an empty can is pushed into water, we feel :
a downward force
an upward force
it is easy to push the can into water
both a downward force and reduced effort while pushing the can into water
Answer
an upward force
Reason / Explanation
The upward force exerted on the empty can by water opposing the push is called upthrust or buoyant force.
Question 2The effect of upthrust is that the weight of a body immersed in a liquid appears to be :
Question
The effect of upthrust is that the weight of a body immersed in a liquid appears to be :
more than its actual weight
the same as its weight outside the liquid
less than its actual weight
None of these
Answer
less than its actual weight
Reason / Explanation
Due to the upthrust or the buoyant force acting on a body immersed in water, the weight of a body appears to be less than its actual weight.
Question 3Which of the following are the correct characteristic properties of upthrust ?
Question
Which of the following are the correct characteristic properties of upthrust ?
(i) the smaller the volume of a body submerged in a liquid, the smaller is the upthrust
(ii) the upthrust acts on the body in an upward direction at the centre of buoyancy
(iii) for the same volume of a body inside a fluid, the less the density of the fluid, greater will be the upthrust
Answer
(i) & (ii)
Reason / Explanation
Characteristic properties of upthrust :
Larger the volume of a body submerged in a fluid, greater is the upthrust.
For the same volume of a body inside a fluid, more the density of fluid, greater is the upthrust.
The upthrust acts on the body in upward direction at the centre of buoyancy i.e., the centre of gravity of the displaced fluid.
Question 4The correct relation for upthrust on a solid of submerged volume V in a liquid of density ρ is: (a) F_B = V/(ρg)
Question
(a) F_B = V/(ρg)
(b) F_B = Vρ/g
(c) F_B = Vρg
(d) F_B = Vg/ρ
Answer
Reason / Explanation
Question 5Archimedes' principle applies on :
Question
Archimedes' principle applies on :
solids and liquids
liquids and gases
solids and gases
solids, liquids and gases
Answer
liquids and gases
Reason / Explanation
Archimedes' principle applies on both, liquids & gases.
Question 6If a body is completely immersed in a liquid, the volume of the liquid displaced will be ............... its own volume and the upthrust will be .......…
Question
If a body is completely immersed in a liquid, the volume of the liquid displaced will be ............... its own volume and the upthrust will be ...............
less than, minimum
equal to, minimum
more than, maximum
equal to, maximum
Answer
equal to, maximum
Reason / Explanation
If a body is completely immersed in a liquid, the volume of the liquid displaced will be equal to its own volume and the upthrust will be maximum.
Question 7The apparent loss in weight is equal to the upthrust on the body verifies :
Question
The apparent loss in weight is equal to the upthrust on the body verifies :
Pascal's law
Newton's third law
Archimedes' principle
Newton's second law
Answer
Archimedes' principle
Reason / Explanation
Archimedes' principle states that when a body is immersed partially or completely in a liquid, it experiences an upthrust, which is equal to the weight of the liquid displaced by it.
Question 8A body weighed 'W' in air by a sensitive spring balance. It will weigh ............... in vacuum.
Question
A body weighed 'W' in air by a sensitive spring balance. It will weigh ............... in vacuum.
the same
slightly more
slightly less
zero
Answer
slightly more
Reason / Explanation
A body weighed 'W' in air by a sensitive spring balance, will weigh slightly more in vacuum, because in vacuum no upthrust acts.
Question 9Floating of a cork on the surface of water indicates that :
Question
Floating of a cork on the surface of water indicates that :
the density of water is more than the density of cork.
the density of water is less than the density of cork.
the density of water is equal to the density of cork.
the density of water plays no role in the floatation of cork.
Answer
the density of water is more than the density of cork.
Reason / Explanation
Bodies of density greater than that of the liquid sink in it, while bodies of average density equal to or smaller than that of the liquid float on it.
Question 10Sinking of an iron nail in water implies that :
Question
Sinking of an iron nail in water implies that :
the density of nail is more than the density of water
the density of nail is less than the density of water
the density of nail is equal to the density of water
the sinking of nail does not depend upon the density of water
Answer
the density of nail is more than the density of water
Reason / Explanation
Bodies of density greater than that of the liquid sink in it, while bodies of average density equal to or smaller than that of the liquid float on it.
Question 11Bodies of density ............... than that of the liquid sink in it, while bodies of average density equal to or ............... than that of the liqui…
Question
Bodies of density ............... than that of the liquid sink in it, while bodies of average density equal to or ............... than that of the liquid float on it.
smaller, greater
greater, greater
greater, smaller
smaller, smaller
Answer
greater, smaller
Reason / Explanation
Bodies of density greater than that of the liquid sink in it, while bodies of average density equal to or smaller than that of the liquid float on it.
Question 12A body will experience minimum upthrust when it is completely immersed in:
Question
A body will experience minimum upthrust when it is completely immersed in:
turpentine
water
glycerine
mercury.
Answer
turpentine
Reason / Explanation
One of the factors affecting the upthrust is the density of the liquid in which the body is submerged. Lesser the density of the liquid, lesser is the upthrust experienced by a body. As amongst the given options turpentine has the least density, hence minimum upthrust will be offered by turpentine.
Question 13A body of density ρ sinks in a liquid of density ρL. The densities ρ and ρL are related as:
Question
A body of density ρ sinks in a liquid of density ρL. The densities ρ and ρL are related as:
ρ < ρL
ρ > ρL
nothing can be said.
Answer
Reason / Explanation
Bodies of density greater than that of liquid, sink in it.
Exercise 5(A) — Very Short Answer Type
9 solved questions
Question 1In what direction and at what point does the buoyant force on a body due to a liquid, act?
Question
In what direction and at what point does the buoyant force on a body due to a liquid, act?
Answer
The buoyant force on a body due to a liquid acts in the upward direction at the center of buoyancy i.e. the centre of gravity of the displaced liquid.
Question 2Define upthrust and state its S.I. unit.
Question
Define upthrust and state its S.I. unit.
Answer
The upward force exerted on a body by the fluid in which it is submerged, is called the upthrust.
The S.I. unit of upthrust is Newton (N).
Question 3Why is a force needed to keep a block of wood inside water?
Question
Why is a force needed to keep a block of wood inside water?
Answer
A force is needed to keep a block of wood inside water because upthrust due to water on block when fully submerged is more than its weight.
Question 4A body experiences an upthrust F1 in river water and F2 in sea water when dipped up to the same level. Which is more F1 or F2 ? Give reason.
Question
A body experiences an upthrust F1 in river water and F2 in sea water when dipped up to the same level. Which is more F1 or F2 ? Give reason.
Answer
As we know that the sea water is denser than river water, and if the density of the liquid is more it exerts more buoyant force. Hence, the body in sea water will experience more upthrust than in river water.
Question 5A body of volume V and density ρ is kept completely immersed in a liquid of density ρL. If g is the acceleration due to gravity, write expressions for t…
Question
A body of volume V and density ρ is kept completely immersed in a liquid of density ρL. If g is 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.
Answer
Given,
Density = ρ
Density of liquid = ρL
Acceleration due to gravity = g
(i) The weight of the body, acting downwards = Vρg
Question 6Complete the following sentences —
Question
Complete the following sentences —
(a) Two balls, one of iron and the other of aluminium 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 2 m 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.
Answer
(a) Two balls, one of iron and the other of aluminium experience the same upthrust when dipped completely in water if both have equal volumes.
(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 remain at the same position.
(c) A piece of wood is held under water. The upthrust on it will be more than the weight of the wood piece.
Question 7A sphere of iron and another of wood of the same radius are held under water. Compare the upthrust on the two spheres.
Question
A sphere of iron and another of wood of the same radius are held under water. Compare the upthrust on the two spheres.
[Hint — Both have equal volume inside water.]
Answer
Let density of water be ρw
Since radius of both spheres are same hence their volume will be equal.
∵ Volume of iron sphere and volume of wood sphere is same hence, upthrust by water acting on both the spheres is same.
Comparing the upthrust on the two spheres:
Upthrust
iron
Vρ
w
g
Vρ
w
g
Upthrust
wood
Upthrust
iron
1
Question 8A body of density ρ is immersed in a liquid of density ρL. State condition when the body will (i) float, (ii) sink, in liquid.
Question
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.
Answer
Question 9State Archimedes' principle.
Question
State Archimedes' principle.
Answer
Archimedes' principle states that when a body is immersed partially or completely in a liquid, it experiences an upthrust, which is equal to the weight of the liquid displaced by it.
Exercise 5(A) — Short Answer Type
13 solved questions
Question 1What is meant by the term buoyancy?
Question
What is meant by the term buoyancy?
Answer
The property of liquid to exert an upward force on a body immersed in it, is called buoyancy.
Question 2What is the cause of upthrust? At which point it can be considered to act?
Question
What is the cause of upthrust? At which point it can be considered to act?
Answer
Upthrust or buoyant force arises due to the differences in pressure acting on the submerged object. The fluid exerts pressure on all sides of the object, and the pressure is greater at greater depths. The pressure difference between the top and bottom of an object creates an upward force (i.e., upthrust) that opposes the weight of the object.
Upthrust acts on the body in upward direction at the centre of buoyancy (i.e., the centre of gravity of the displaced liquid).
Question 3State three characteristic properties of upthrust.
Question
State three characteristic properties of upthrust.
Answer
The upthrust has the following three characteristic properties:
Larger the volume of a body submerged in a fluid, greater is the upthrust.
For the same volume of a body inside a fluid, more the density of fluid, greater is the upthrust.
The upthrust acts on the body in upward direction at the centre of buoyancy i.e., the centre of gravity of the displaced fluid.
Question 4A piece of wood if left under water, comes to the surface. Explain the reason.
Question
A piece of wood if left under water, comes to the surface. Explain the reason.
Answer
When a piece of wood is left under water, two forces act on it, (i) its weight (i.e., the force due to gravity) W which pulls it downwards, and (ii) the upthrust FB due to water which pushes the wood upwards. The piece of wood comes to the surface because upthrust on the wood is more than the weight of the wood (i.e.,FB > W ).
Question 5Will a body weigh more in air or in vacuum when weighed with a spring balance? Give a reason for your answer.
Question
Will a body weigh more in air or in vacuum when weighed with a spring balance? Give a reason for your answer.
Answer
A body weighs more in vacuum than in air when weighed with a spring balance because an upthrust acts on the body in air due to which it appears lighter than its actual weight.
Question 6A 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.…
Question
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.
Answer
When a metal solid cylinder tied to a thread, hanging from the hook of a spring balance is gradually immersed into water contained in a jar, then it is observed that the readings on the spring balance decrease.
This loss of weight is due to the upthrust (or buoyant force) of water on the cylinder, hence the reading decreases and the cylinder appears to be lighter.
Question 7A body dipped into a liquid experiences an upthrust. State two factors on which upthrust on the body depends.
Question
A body dipped into a liquid experiences an upthrust. State two factors on which upthrust on the body depends.
Answer
The factors on which upthrust on the body depends are —
Volume of the body immersed in the liquid (fluid), and
Density of the liquid (fluid) in which the body is submerged.
Question 8How is the upthrust related to the volume of the body submerged in a liquid ?
Question
How is the upthrust related to the volume of the body submerged in a liquid ?
Answer
Larger the volume of a body submerged in a fluid, greater is the upthrust.
Question 9A bunch of feathers and a stone of the same mass are released simultaneously in air. Which will fall faster and why? How will your observation be differ…
Question
A bunch of feathers and a stone of the same mass are released simultaneously in air. Which will fall faster and why? How will your observation be different if they are released simultaneously in vacuum ?
Answer
When a bunch of feathers and a stone of same mass are allowed to fall in air, the stone falls faster than the bunch of feathers.
The reason is that upthrust due to air on stone is less than that on the bunch of feathers because the volume of stone is less than that of the bunch of feathers of same mass.
If they both are released simultaneously in vacuum, they will fall together because there will be no upthrust.
Question 10A 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 differ…
Question
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.
Answer
When we place a small block of wood in water and another identical block of wood in glycerine, we notice that both the blocks float but the volume of block immersed in glycerine is smaller as compared to the volume of block immersed in water.
The reason is that the density of glycerine is more than that of water and so it exerts more buoyant force and hence, less part of block is immersed.
Question 11A sphere of iron and another of wood, both of same radius are placed on the surface of water. State which of the two will sink? Give reason to your answer.
Question
A sphere of iron and another of wood, both of same radius are placed on the surface of water. State which of the two will sink? Give reason to your answer.
Answer
When a sphere of iron and wood are placed in water then the sphere of iron will sink.
Question 12How does the density of material of a body determine whether it will float or sink in water?
Question
How does the density of material of a body determine whether it will float or sink in water?
Answer
The bodies of density greater than that of the liquid sink in it, while bodies of average density equal to or smaller than that of the liquid float on it.
Question 13It is easier to lift a heavy stone under water than in air. Explain.
Question
It is easier to lift a heavy stone under water than in air. Explain.
Answer
It is easier to lift a heavy stone under water than in air because due to the effect of upthrust, the stone experiences an upward buoyant force that balances the true weight of the stone which is acting in the opposite direction.
Hence, the weight of the stone immersed in water appears less than the actual weight.
Exercise 5(A) — Long Answer Type
5 solved questions
Question 1What do you understand by the term upthrust of a fluid? Describe an experiment to show its existence.
Question
What do you understand by the term upthrust of a fluid? Describe an experiment to show its existence.
Answer
The upward force exerted on a body by the fluid in which it is submerged is called upthrust or buoyant force.
Experiment —
If a piece of cork is placed on a surface of water in a tub, it floats with nearly
2
5
2
of its volume inside the water. If the cork is pushed into the water and then released, it again comes to the surface of water and floats.
If the cork is kept immersed, our fingers experience some upward force. This upward force is the buoyant force.
Question 2Describe an experiment to show that a body immersed in a liquid appears lighter than it really is.
Question
Describe an experiment to show that a body immersed in a liquid appears lighter than it really is.
Answer
The weight of body immersed in a liquid appears to be less than its actual weight due to the effect of upthrust.
Experiment
Lifting of a bucket full of water from a well —
Take an empty bucket and tie a long rope to it. If the bucket is immersed in the water of a well keeping one end of rope in hand and the bucket is pulled when it is deep inside water, we notice that it is easy to pull the bucket as long as it is inside water.
But as soon it starts coming out of the water surface, it appears to become heavier and now more force is needed to lift it.
This experiment shows that the weight of body appears lighter when it is immersed in water than its actual weight (in air).
Question 3A 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…
Question
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 acting on the body and state the conditions when the body will float or sink.
Answer
Below diagram shows the direction of forces acting on a body completely immersed inside a liquid:
Whether the body will float or sink will depend on the relative values of F1 and F2.
Question 4Prove 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 becau…
Question
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 liquid on the upper and lower surfaces of the submerged part of the body.
Answer
Consider a cylindrical body PQRS of cross-sectional area A immersed in a liquid of density ρ as shown in the figure. Let the upper surface PQ of body be at a depth h1 while its lower surface RS be at a depth h2 below the free surface of liquid.
At depth h1, the pressure on the upper surface PQ
At depth h2, the pressure on the lower surface RS
The horizontal thrust at various points on the vertical sides of the body get balanced because liquid pressure is same at all points at the same depth.
Resultant upward thrust on the body
Since a solid when immersed in a liquid, displaces liquid equal to the volume of its submerged part, therefore
Hence,
Now in another experiment, we suspend a solid by a thin thread attached to the hook of a spring balance to check its weight. Once the weight is noted, we fill a eureka can with water till its spout and place a measuring cylinder below the spout of the eureka can. The solid is then immersed in water and the displaced water is collected in the cylinder.
When the water stops dripping, the weight of the solid and the volume of water in the cylinder are noted.
In the above figure, the solid weighs 300 gf in air and 200 gf when it is completely immersed in water. The volume of water collected in the measuring cylinder is 100 ml i.e., 100 cm3
From equations 1 and 2,
Thus, the weight of water displaced by a solid is equal to the loss in weight of solid.
Question 5Describe an experiment to verify Archimedes' principle.
Question
Describe an experiment to verify Archimedes' principle.
Answer
Experiment —
Take a solid (say a metallic piece). Suspend a solid by a thin thread from the hook of a spring balance. Note its weight. Now take a eureka can and fill it with water to its spout. Arrange a measuring cylinder below the spout of the eureka can.
Now, immerse the solid gently into water of the eureka can. The water displaced by it gets collected in the measuring cylinder, as shown in figure. When water stops dripping through the spout, note the weight of the solid and the volume of water collected in the measuring cylinder.
As shown in figure, the solid weighs 300 gf in air and 200 gf when it is completely immersed in water. The volume of water collected in the ,measuring cylinder is 100 ml i.e., 100 cm3.
From eqns. (i) and (ii)
Thus, the weight of water displaced by a solid is equal to the loss in weight of the solid. This verifies Archimedes' principle.
Exercise 5(A) — Numericals
10 solved questions
Question 1A body of volume 100 cm3 weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 × 103 kg m−3. Find : (i) the upthrust due to liquid a…
Question
A body of volume 100 cm3 weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 × 103 kg m−3. Find : (i) the upthrust due to liquid and (ii) the Weight of the body in liquid.
Answer
(i) As we know,
Given,
Weight of the body in air = 5 kgf
Density of the liquid = 1.8 × 103 kg m−3
Converting cm3 into m3
Substituting the values in the formula above we get,
Substituting the values in the formula above, we get,
Question 2A body weighs 450 gf in air and 310 gf when completely immersed in water.
Question
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).
Answer
Given,
Weight in water = 310 kgf
Loss in weight = 450 – 310 = 140 gf
Density of water = 1 g cm−3
Substituting the values in the formula above, we get,
Question 3You are provided with a hollow iron ball A of volume 15 cm3 and mass 12 g and a solid iron ball B of mass 12 g. Both are placed on the surface of water…
Question
Answer
Mass
density
Mass
[Equation 2]
Given,
Mass of ball B = 12 g
Volume of the hollow iron ball A = 15 cm3
Density of iron = 8 g cm3
Substituting the values in equation 2, to find volume of solid iron ball B,
12
8
12
Substituting the values in equation 1 to get upthrust on hollow ball A
Substituting the values in equation 1 to get upthrust on solid iron ball B
(b) Solid iron ball B will sink.
Ball B experiences an upthrust of 1.5 gf in water that is less than its weight of 12 gf. Hence ball B will sink.
Ball A experiences an upthrust of 15 gf that is greater than its weight of 12 gf. Hence it will float with its that much part submerged for which upthrust becomes equal to its weight of 12 gf.
Question 4A solid of density 5000 kg m−3 weighs 0.5 kgf in air. It is completely immersed in water of density 1000 kg m−3. Calculate the apparent weight of the so…
Question
A solid of density 5000 kg m−3 weighs 0.5 kgf in air. It is completely immersed in water of density 1000 kg m−3. Calculate the apparent weight of the solid in water.
Answer
and
Mass
density
Mass
[Equation 2]
Given,
Weight of the solid = 0.5 kgf
Density of water = 1000 kg m−3
Substituting the values in equation 2 to get volume
0.5
5000
0.5
Substituting the values in the formula above we get,
Substituting the values we get,
Question 5Two spheres A and B, each of volume 100 cm3 are placed on water (density = 1.0 g cm−3). The sphere A is made of wood of density 0.3 g cm−3 and the spher…
Question
(a) Find (i) the weight of each sphere, and (ii) the upthrust on each sphere.
(b) Which sphere will float ? Give reason.
Answer
(a)
Given,
Density of sphere A = 0.3 g cm−3
Density of sphere B = 8.9 g cm−3
Volume of sphere A & B = 100 cm3
Substituting the values in the formula 1, we get weight of sphere A and B,
(ii) Substituting the values in the formula 2, we get upthrust on A and B,
(b) Sphere A will float.
The upthrust on sphere A is 100 gf which is more than its weight of 30 gf hence sphere A will float with its that much part submerged for which upthrust becomes equal to its weight of 30 gf.
The upthrust on sphere B is also 100 gf but it is less than its weight of 890 gf hence sphere B will sink. In general, if the density of the body is less than the density of the liquid then it will float, and as the density of wood is lesser than the density of water hence sphere A floats.
Question 6The mass of a block made of a certain material is 13.5 kg and its volume is 15 × 10−3 m3.
Question
The mass of a block made of a certain material is 13.5 kg and its volume is 15 × 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 reason for your answer.
Answer
Given,
Volume of block = 15 × 10−3 m3
Density of water = 1000 kg m−3
Substituting the values in the formula above, we get, upthrust on block,
(b) The upthrust on the block when fully immersed is 15 kgf which is more than its weight of 13.5 kgf hence the block will float in water when released.
(c) The block will float with its that much part submerged for which upthrust becomes equal to its weight of 13.5 kgf. Hence while floating, upthrust on the block will be 13.5 kgf.
Question 7A piece of brass weighs 175 gf in air and 150 gf when fully immersed in water. The density of water is 1.0 g cm−3. (i) What is the volume of the brass p…
Question
A piece of brass weighs 175 gf in air and 150 gf when fully immersed in water. The density of water is 1.0 g cm−3. (i) What is the volume of the brass piece? (ii) Why does the brass piece weigh less in water?
Answer
Given,
Weight of the brass piece in water = 150 gf
Density of water = 1.0 g cm−3
(i) Upthrust on brass piece = volume of brass piece × density of water × g
and
(ii) The brass piece weighs lesser in water due to the upthrust.
The brass piece experiences an upward buoyant force that balances the true weight of the piece which is acting in the opposite direction.
Hence, the weight of the brass piece immersed in water appears less than the actual weight.
Question 8A metal cube of edge 5 cm and density 9.0 g cm−3 is suspended by a thread so as to be completely immersed in a liquid of density 1.2 g cm−3. Find the te…
Question
Answer
Given,
= 125 × 1.2 × g
= 150 gf
= true weight – upthrust
= 1125 − 150
= 975 gf
= 9.75 N [∵ g = 10 m s−2]
Question 9A block of wood is floating on water with its dimensions 50 cm × 50 cm × 50 cm inside water. Calculate the buoyant force acting on the block. Take g = 9…
Question
Answer
Given,
Question 10A body of mass 3.5 kg displaces 1000 cm3 of water when fully immersed inside it. Calculate (i) the volume of body, (ii) the upthrust on body and (iii) t…
Question
A body of mass 3.5 kg displaces 1000 cm3 of water when fully immersed inside it. Calculate (i) the volume of body, (ii) the upthrust on body and (iii) the apparent weight of body in water.
Answer
Given,
Therefore, weight = 3.5 kgf
= 1000 × 0.001 × g
= 1 kgf
= 3.5 − 1
= 2.5 kgf
Exercise 5(B) — Multiple Choice Type
8 solved questions
Question 1The effect of temperature on density is that it :
Question
The effect of temperature on density is that it :
decreases with an increase in temperature
increases with an increase in temperature
first decreases then increases with a decrease in temperature
is not affected by temperature
Answer
decreases with an increase in temperature
Reason / Explanation
Most of the substances expand on heating and contract on cooling, but their mass remains unchanged. Therefore, density of most of the substances decreases with the increase in temperature and increases with the decrease in temperature.
Question 2The mass of 1 cm³ of iron is 7.8 g. Its density in S.I. units is: (a) 7.8 kg cm⁻³
Question
Answer
7800 kg m⁻³
Reason / Explanation
Question 3The density of water is maximum at ............... °C and is ............... kg/m3
Question
The density of water is maximum at ............... °C and is ............... kg/m3
0, 1
0, 1000
4, 1
4, 1000
Answer
4, 1000
Reason / Explanation
Due to anomalous expansion of water, when cooled it first contracts in volume but below 4°C, it starts expanding and continues to do so till the temperature reaches 0°C, the point at which it freezes into ice. Thus, The density of water is maximum at 4°C and is 1000 kg/m3.
Question 4Relative density of a substance is expressed by comparing the density of that substance with the density of:
Question
Relative density of a substance is expressed by comparing the density of that substance with the density of:
air
mercury
water
iron
Answer
water
Reason / Explanation
Relative density of a substance is also defined as the ratio of the mass of a certain volume of a substance to the mass of an equal volume of water at 4°C.
Question 5The unit of relative density is:
Question
The unit of relative density is:
g cm−3
kg m−3
m3 kg−1
no unit
Answer
no unit
Reason / Explanation
Since relative density is a pure ratio, it has no unit.
Question 6The correct relation between density and relative density in the C.G.S. system is: R.D. = density of substance in g cm⁻³ ÷ 1.0 g cm⁻³
Question
R.D. = density of substance in g cm⁻³ ÷ 1.0 g cm⁻³
Answer
Reason / Explanation
The density of water at 4°C is 1.0 g cm⁻³. Relative density is the ratio of the density of the substance to the density of water at 4°C.
Question 7If the weight of a body in air is W_1 and its weight in water is W_2, the relative density of the body is: (a) W_2/(W_1−W_2)
Question
Answer
Reason / Explanation
Question 8If a body's weight in air, liquid and water is W_1, W_2 and W_3 respectively, then the relative density of the liquid is: R.D. of liquid = (W_1 − W_2) ÷…
Question
R.D. of liquid = (W_1 − W_2) ÷ (W_1 − W_3)
Answer
Reason / Explanation
The numerator is the loss in weight in the liquid, and the denominator is the loss in weight in water.
Exercise 5(B) — Very Short Answer Type
9 solved questions
Question 1Define the term density.
Question
Define the term density.
Answer
The density of a substance is its mass per unit volume. i.e.,
It is a scalar quantity and is represented by the letter ρ (rho) or d.
Question 2What are the units of density in (i) C.G.S. and (ii) S.I. system.
Question
What are the units of density in (i) C.G.S. and (ii) S.I. system.
Answer
(i) In C.G.S system, unit of density is g cm−3.
(ii) In S.I. system, unit of density is kg m−3.
Question 3Express the relationship between the C.G.S. and S.I. units of density.
Question
Express the relationship between the C.G.S. and S.I. units of density.
Answer
Relation between S.I. and C.G.S. units —
1kg
1000g
g cm−3
Thus,
Question 4The density of iron is 7800 kg m−3. What do you understand by this statement?
Question
The density of iron is 7800 kg m−3. What do you understand by this statement?
Answer
The statement tells that the mass of 1 m3 of iron is 7800 kg.
Question 5Write the density of water at 4°C in S.I. unit.
Question
Write the density of water at 4°C in S.I. unit.
Answer
The density of water at 4°C in S.I. unit is 1000 kg m−3.
Question 6How are the (i) mass, (ii) volume, and (iii) density of a metallic piece affected, if at all, with increase in temperature?
Question
How are the (i) mass, (ii) volume, and (iii) density of a metallic piece affected, if at all, with increase in temperature?
Answer
The parameters are affected in the following ways —
(i) Mass — It remains unchanged with increase in temperature.
(ii) Volume — It increases with an increase in the temperature.
(iii) Density — Most of the substances expand on heating and contract on cooling, but their mass remains unchanged. Therefore, density of most of the substances decreases with the increase in temperature.
Question 7Complete the following sentences —
Question
Complete the following sentences —
(ii) S.I. unit of density is ............... .
(iii) Density of water is ............... kg m−3
Answer
(ii) S.I. unit of density is kg m−3
(iii) Density of water is 1000 kg m−3
Question 8What is the unit of relative density?
Question
What is the unit of relative density?
Answer
Relative density has no unit.
Question 9A 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 de…
Question
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 material of the body.
Answer
Given,
(i) Let V be the volume of the body.
But weight of water displaced is equal to upthrust
(iii) Relative density of the material of the body
Weight of solid in air
Weight in air − Weight in water
Weight of solid in air
−W
2
W
1
Exercise 5(B) — Short Answer Type
4 solved questions
Question 1Water is heated from 0°C to 10°C. How does the density of water change with temperature?
Question
Water is heated from 0°C to 10°C. How does the density of water change with temperature?
Answer
On heating from 0°C, the density of water increases up to 4°C and then decreases beyond 4°C.
Question 2What do you understand by the term relative density of a substance?
Question
What do you understand by the term relative density of a substance?
Answer
Relative density of a substance is defined as the ratio of the mass of a certain volume of a substance to the mass of an equal volume of water at 4°C.
Question 3Define relative density as a ratio of mass?
Question
Define relative density as a ratio of mass?
Answer
Relative density is also defined as a ratio of mass of a certain volume of a substance to the mass of an equal volume of water at 4°C.
Question 4Differentiate between density and relative density of a substance?
Question
Differentiate between density and relative density of a substance?
Answer
Density Relative density
Density of a substance is the mass per unit volume of that substance. Relative density of a substance is the ratio of density of that substance to the density of water at 4°C.
It is expressed in g cm−3 or kg m−3. It has no unit.
Exercise 5(B) — Long Answer Type
3 solved questions
Question 1With the use of Archimedes' principle, state how you will find relative density of a solid denser than water and insoluble in it. How will you modify yo…
Question
With the use of Archimedes' principle, state how you will find 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?
Answer
Relative density of a solid denser than water and insoluble in it
Procedure —
(i) Suspend a piece of the given solid with a thread from hook of the left pan of a physical balance and find its weight W1.
(ii) Now balance a wooden bridge over the left pan of balance and place a beaker nearly two-third filled with water on the bridge. Take care that the bridge and beaker do not touch the pan of balance,
(iii) Immerse the solid completely in water such that it does not touch the walls and bottom of beaker and find the weight W2 of solid in water.
Observation —
Calculation —
or
R.D.
−W
2
W
1
Relative density of a solid denser than water and soluble in it —
Procedure —
If solid is soluble in water, instead of water, we take a liquid of known relative density in which solid in insoluble and it sinks in that liquid. Then the process described above is repeated. Now
×R.D. of liquid
Question 2Describe an experiment, using Archimedes' principle, to find the relative density of a liquid.
Question
Describe an experiment, using Archimedes' principle, to find the relative density of a liquid.
Answer
By definition, relative density of a liquid is given as —
By Archimedes' Principle if a solid is immersed in a liquid or water, it displaces the liquid or water equal to its volume. Therefore, above equation takes the form —
(Weight of body)
air
−(Weight of body)
water
(Weight of body)
air
−(Weight of body)
liquid
Thus, to find the relative density of a liquid using Archimedes' Principle, we take a body which is heavier than both the given liquid and water and also insoluble in both. The body is first weighed in air, then in liquid and then after washing it with water and drying, it is weighed in water. If the weight of the body in air is W1 gf, in liquid is W2 gf and in water is W3 gf, then from above we get,
R.D. of liquid=
W
1
−W
3
W
1
−W
2
Question 3A 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…
Question
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.
Answer
Given,
Weight of the body in liquid = W2 gf
Weight of the body in water = W3 gf
(i) Let V be the volume of the body.
But weight of water displaced is equal to upthrust due to water
(iii) Relative density of the solid
−(Weight of body)
water
(Weight of body)
air
W
1
−W
3
W
1
(iv) Relative density of the liquid
−(Weight of body)
water
(Weight of body)
air
−(Weight of body)
liquid
W
1
−W
3
W
1
−W
2
Exercise 5(B) — Numericals
16 solved questions
Question 1The density of copper is 8.83 g cm−3. Express it in kg m−3.
Question
The density of copper is 8.83 g cm−3. Express it in kg m−3.
Answer
Given,
Converting g cm−3 into kg m−3,
Therefore,
8.83
g
10
−3
kg
10
3
kg
Question 2The relative density of mercury is 13.6. State its density in (i) C.G.S. unit, (ii) S.I. unit.
Question
The relative density of mercury is 13.6. State its density in (i) C.G.S. unit, (ii) S.I. unit.
Answer
Given,
(i) In C.G.S. unit,
Density of substance in g cm
Density of substance in g cm
−3
Substituting the values we get,
=
Density of substance in g cm
Density of substance in g cm
Density of substance in g cm
Density of substance in g cm
−3
−3
=13.6×1.0 g cm
−3
−3
=13.6 g cm
−3
(ii) In S.I. unit,
=
Density of substance in kg m
Density of substance in kg m
Density of substance in kg m
Density of substance in kg m
−3
−3
=13.6×1000 kg m
−3
⇒Density of substance in kg m
−3
=13.6×10
−3
kg m
−3
Question 3The density of iron is 7.8 × 103 kg m−3. What is its relative density ?
Question
The density of iron is 7.8 × 103 kg m−3. What is its relative density ?
Answer
We know,
Density of substance in kg m
Density of substance in kg m
−3
Given,
Substituting the values in the formula above we get,
7.8
7.8×1000 kg m
−3
Question 4The relative density of silver is 10.8. Find its density.
Question
The relative density of silver is 10.8. Find its density.
Answer
We know,
Density of substance in kg m
Density of substance in kg m
−3
Given,
Substituting the values in the formula above we get,
Density of silver
−3
Question 5Calculate the mass of a body whose volume is 2 m3 and relative density is 0.52.
Question
Calculate the mass of a body whose volume is 2 m3 and relative density is 0.52.
Answer
As we know,
Given,
R.D. = 0.52
Now,
Density of substance in kg m
Density of substance in kg m
−3
Substituting the values in the formula for R.D. we get,
Density of body
1000 kg m
Density of body
Therefore,
Substituting the values in the formula for mass, we get,
Mass=0.52×1000×2
⇒Mass=1040 kg
Question 6Calculate the mass of air in a room of dimensions 4.5 m × 3.5 m × 2.5 m if the density of air at N.T.P. is 1.3 kg m−3
Question
Calculate the mass of air in a room of dimensions 4.5 m × 3.5 m × 2.5 m if the density of air at N.T.P. is 1.3 kg m−3
Answer
Given,
Dimensions of room = 4.5 m × 3.5 m × 2.5 m
∴ Volume of room = 4.5 × 3.5 × 2.5 = 39.375 m3
= 1.3 × 39.375
= 51.1875 kg
Question 7A piece of stone of mass 113 g sinks to the bottom in water contained in a measuring cylinder and water level in cylinder rises from 30 ml to 40 ml. Cal…
Question
A piece of stone of mass 113 g sinks to the bottom in water contained in a measuring cylinder and water level in cylinder rises from 30 ml to 40 ml. Calculate R.D. of stone.
Answer
Given,
Rise in the level of water is equivalent to the volume occupied by the stone
10
113
−3
Density of stone in g cm
−3
1
11.3
Question 8A body of volume 100 cm3 weighs 1 kgf in air. Find (i) its weight in water and (ii) its relative density.
Question
A body of volume 100 cm3 weighs 1 kgf in air. Find (i) its weight in water and (ii) its relative density.
Answer
Given,
Weight of the body in air (W1) = 1 kgf = 1000 gf
Let weight of the body in water be W2
Density
100
1000
−3
Hence,
Density of body in g cm
−3
1
10
R.D. of body=
W
1
−W
2
W
1
1000−W
2
1000
2
⇒10000−10W
2
⇒10W
2
⇒W
2
10
9000
2
Hence,
Question 9A body of mass 70 kg, when completely immersed in water, displaces 20,000 cm3 of water. Find : (i) the weight of body in water and (ii) the relative den…
Question
A body of mass 70 kg, when completely immersed in water, displaces 20,000 cm3 of water. Find : (i) the weight of body in water and (ii) the relative density of material of body.
Answer
Given,
Volume of water displaced = 20,000 cm3
Converting cm3 to m3, we get,
= 0.02 × 1000
= 20 kg
Weight of water displaced = mg = 20 × g = 20 kgf
Weight of body in water = weight of body in air − upthrust due to liquid
= 70 kgf − 20 kgf [∵ upthrust is equal to weight of water displaced]
= 50 kgf
(ii) Formula for density is:
0.02
70
−3
Density of body in kg m
−3
1000
3500
Question 10A solid weighs 120 gf in air and 105 gf when it is completely immersed in water. Calculate the relative density of solid.
Question
A solid weighs 120 gf in air and 105 gf when it is completely immersed in water. Calculate the relative density of solid.
Answer
Given,
Relative density of solid=(
W
1
−W
2
W
1
=(
120−105
120
=8
Question 11A 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 densi…
Question
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 0.9 g cm−3.
Answer
Given,
−W
2
W
1
=(
32−28.8
32
=(
3.2
32
=10
But, R.D. of solid=
1 g cm
−3
Density of solid in g m
−3
1 g cm
−3
Density of solid in g m
−3
−3
Volume
Mass
Density
Mass
10
32
3
Let weight of solid in liquid of density 0.9 g cm−3 be W.
R.D. of liquid
R.D. of solid=(
W
1
−W
2
W
1
)×R.D. of liquid
And
Density of liquid in g cm
−3
1
0.9
Substituting the values in the formula for relative density of solid :
10=
32−W
28.8
10×(32−W)=28.8
320−10W=28.8
10W=320−28.8
W=
10
291.2
Summarizing the answers:
Question 12A body weighs 20 gf in air and 18.0 gf in water. Calculate relative density of the material of the body.
Question
A body weighs 20 gf in air and 18.0 gf in water. Calculate relative density of the material of the body.
Answer
Given,
−W
2
W
1
=(
20−18
20
=(
2
20
=10
Question 13A solid weighs 1.5 kgf in air and 0.9 kgf in a liquid of density 1.2 × 103 kg m−3. Calculate R.D. of solid.
Question
A solid weighs 1.5 kgf in air and 0.9 kgf in a liquid of density 1.2 × 103 kg m−3. Calculate R.D. of solid.
Answer
Given,
Density of liquid in kg m
−3
And
R.D. of solid
R.D. of liquid
=
(
1.5
−
0.9
)
×
1.2
=
(
1.5
0.6
)
R.D. of solid=(
W
1
−W
2
W
1
=(
1.5−0.9
1.5
=(
0.6
1.5
=3.0
Question 14A jeweller 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 wei…
Question
A jeweller 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 material of bangle which comes out to be 11.6].
Answer
Given,
−W
2
W
1
=(
25.25−23.075
25.25
=(
2.175
25.25
=11.6
It is given that relative density of gold is 19.3 where as relative density of bangle is 11.6.
Hence, we can deduce that the bangle is not made of pure gold.
Question 15A piece of iron weighs 44.5 gf in air. If the density of iron is 8.9 × 103 kg m−3, find the weight of the iron piece when immersed in water.
Question
A piece of iron weighs 44.5 gf in air. If the density of iron is 8.9 × 103 kg m−3, find the weight of the iron piece when immersed in water.
Answer
Given,
Density of iron in kg m
−3
From relation,
R.D.
−W
2
W
1
44.5−W
2
44.5
2
⇒(8.9×44.5)−(8.9W
2
⇒396.05−8.9W
2
⇒W
2
8.9
396.05−44.5
2
8.9
351.55
2
Question 16A piece of stone of mass 15.1 g 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. Ca…
Question
A piece of stone of mass 15.1 g 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 air,
(b) the volume of the piece of stone,
(c) the relative density of stone,
(d) the relative density of the liquid.
Answer
Given,
(b) Upthrust on the stone
Let volume of the piece of stone be V.
From the relation,
⇒ V = 5.4 cm3
(c) From the relation,
Relative density of stone
=
(
W
1
W
1
−
W
3
)
=
(
15.1
−
9.7
)
=
(
15.1
5.4
)
=
2.79
≈
2.8
Relative density of stone=(
W
1
−W
3
W
1
=(
15.1−9.7
15.1
=(
5.4
15.1
=2.79≈2.8
(d) From the relation,
Relative density of liquid=
W
1
−W
3
W
1
−W
2
where,
W1 is the weight of piece of stone in air,
W2 is the weight of piece of stone in liquid,
W3 is the weight of piece of stone in water
Substituting the values in the formula above we get,
Relative density of liquid
=
15.1
−
10.9
15.1
−
9.7
=
4.2
5.4
=
0.777
≈
0.78
Relative density of liquid=
15.1−9.7
15.1−10.9
5.4
4.2
Exercise 5(C) — Multiple Choice Type
15 solved questions
Question 1(i)The upthrust is maximum (= FB) when the body is:
Question
floating in the liquid
completely immersed inside the liquid
partially immersed inside the liquid
None of these
Answer
completely immersed inside the liquid
Reason / Explanation
Hence, FB will be maximum when the body is completely immersed inside the liquid.
Question 1(ii)A body weighing W floats partially above and partially below the liquid when (FB denotes maximum upthrust) :
Question
A body weighing W floats partially above and partially below the liquid when (FB denotes maximum upthrust) :
W = FB
W < FB
none of these
Answer
W < FB
Reason / Explanation
When a body weighing W floats partially above and partially below the liquid, it implies that the weight of the body is less than the maximum upthrust experienced by it when fully immersed inside the liquid.
Hence, W < FB.
Question 1(iii)A body of weight W is floating in a liquid. Its apparent weight will be:
Question
A body of weight W is floating in a liquid. Its apparent weight will be:
equal to W
less than W
greater than W
zero
Answer
zero
Reason / Explanation
Question 1(iv)For a floating body of total volume V and submerged volume v, with body density ρ_S and liquid density ρ_L, the correct relation is: (a) v/V = ρ_S/ρ_L
Question
(a) v/V = ρ_S/ρ_L
(b) V/v = ρ_S/ρ_L
(c) vρ_S = Vρ_L
(d) None of these
Answer
Reason / Explanation
Question 1(v)A 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 liquid. The…
Question
A 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 liquid. The densities ρ1 and ρ2 are related as:
ρ1 < ρ2
ρ1 > ρ2
nothing can be said
Answer
Reason / Explanation
Density of liquid A (ρ1) is greater than the density of liquid B (ρ2) as the body is partially immersed in liquid A whereas it is fully immersed in liquid B.
Question 1(vi)Every ship has a white line painted on its side known as :
Question
Every ship has a white line painted on its side known as :
Plimsoll line
Border line
Harbour line
None of the above
Answer
Plimsoll line
Reason / Explanation
Plimsoll line indicates the safe limit for loading the ship in water of density 103 kg m−3. A ship is not allowed to load further if its plimsoll line starts touching the water level, so that when it sails in sea water of density more than 103 kg m−3, only the part of it below the plimsoll line remains submerged in water.
Question 1(vii)Which of the following statements is correct ?
Question
Which of the following statements is correct ?
(i) A loaded ship is submerged more while an unloaded ship is submerged less.
(ii) A ship begins to be less submerged as it sails from sea water to river water.
only (i)
only (ii)
both (i) and (ii)
both are incorrect
Answer
only (i)
Reason / Explanation
A loaded ship is submerged more while an unloaded ship is submerged less because loaded ship has more weight and exerts more force vertically downwards.
A ship begins to be submerged more as it sails from sea water to river water. The water of a river is of low density than that of a sea. Therefore, a ship sails from sea water to river water, it sinks further. The reason is that according to the law of floatation, to balance the weight of ship, a greater volume of water is required to be displaced in water of lower density in river.
Question 1(viii)An unloaded ship is filled with sand at its bottom to ............... its centre of gravity and make its equilibrium ...............
Question
An unloaded ship is filled with sand at its bottom to ............... its centre of gravity and make its equilibrium ...............
lower, unstable
higher, stable
lower, stable
higher, unstable
Answer
lower, stable
Reason / Explanation
An unloaded ship floats with very small volume inside water. As a result, its centre of gravity is higher and its equilibrium is unstable. There is a danger that it may get blown over on its side by strong winds. Therefore, an unloaded ship is filled with sand (or stones), called ballast, at its bottom. This lowers its centre of gravity to make its equilibrium stable.
Question 1(ix)It is easier for humans to swim in sea water than in river water as :
Question
It is easier for humans to swim in sea water than in river water as :
the density of sea water is less than that of the river water.
the density of sea water is more than that of river water.
the sea is big in comparison to the river.
None of the above
Answer
the density of sea water is more than that of river water
Reason / Explanation
It is easier to swim in sea water because the density of sea water is more than that of the river water, so our weight is balanced in sea water with less part of the body submerged inside it.
Question 1(x)If a submarine is to dive, its ballast tanks are ..............., so that the average density of the submarine becomes ............... than the density…
Question
If a submarine is to dive, its ballast tanks are ..............., so that the average density of the submarine becomes ............... than the density of sea water.
filled with water, greater
filled with water, lower
emptied, greater
emptied, lower
Answer
filled with water, greater
Reason / Explanation
If a submarine is to dive, its ballast tanks are, filled with water so that the average density of the submarine becomes greater than the density of sea water
Question 1(xi)Ice bergs float on the surface of water with their ............... portion inside the water surface and ............... portion above the water surface.
Question
Ice bergs float on the surface of water with their ............... portion inside the water surface and ............... portion above the water surface.
smaller, larger
larger, equal
smaller, smaller
larger, smaller
Answer
larger, smaller
Reason / Explanation
As ice bergs are lighter than water, they float on the surface of water with their larger portion inside the water surface and smaller portion above the water surface.
Question 1(xii)A balloon does not rise indefinitely because :
Question
A balloon does not rise indefinitely because :
the density of air increases with altitude
the density of air decreases with altitude
the weight of the displaced air increases.
None of the above
Answer
the density of air decreases with altitude
Reason / Explanation
A balloon does not rise indefinitely because the density of air decreases with altitude. Therefore, as the balloon gradually goes up, the weight of the displaced air decreases. It keeps on rising as long as the upthrust on it exceeds its weight. When upthrust becomes equal to its weight, it stops rising further.
Question 1(xiii)When a fish has to rise up in water, it diffuses oxygen gas from its blood into the bladder, so its volume ............... and its average density .....…
Question
When a fish has to rise up in water, it diffuses oxygen gas from its blood into the bladder, so its volume ............... and its average density ............... .
decreases, decreases
increases, decreases
decreases, increases
increases, increases
Answer
increases, decreases
Reason / Explanation
When a fish has to rise up in water, it diffuses oxygen gas from its blood into the bladder, so its volume increases and its average density decreases
This increases the volume of water displaced by the fish and so the upthrust on the fish increases due to which it rises up.
Question 1(xiv)A ball has density ρ such that ρ_oil < ρ < ρ_water. Oil and water are immiscible. Where will the ball come to rest?
Question
A ball has density ρ such that ρ_oil < ρ < ρ_water. Oil and water are immiscible. Where will the ball come to rest?
Answer
The ball comes to rest at the oil–water interface, partly in oil and partly in water.
Reason / Explanation
The ball is denser than oil, so it sinks through oil. It is less dense than water, so it floats on water. Therefore, equilibrium occurs at the interface.
Question 1(xv)An object floats with 1/9, 2/11 and 3/7 of its volume outside liquids A, B and C respectively. Arrange the liquid densities ρ_1, ρ_2 and ρ_3 in increasi…
Question
(a) ρ_1 > ρ_2 > ρ_3
(b) ρ_2 > ρ_3 > ρ_1
(c) ρ_3 > ρ_2 > ρ_1
(d) ρ_3 > ρ_1 > ρ_2
Answer
Reason / Explanation
Exercise 5(C) — Very Short Answer Type
8 solved questions
Question 1State the principle of floatation.
Question
State the principle of floatation.
Answer
The principle of floatation states that the weight of a floating body is equal to the weight of the liquid displaced by its submerged part.
Question 2When a piece of wood is suspended from the hook of a spring balance, it reads 70 gf. The wood is now lowered into water. What reading do you expect on t…
Question
When a piece of wood is suspended from the hook of a spring balance, it reads 70 gf. The wood is now lowered into water. What reading do you expect on the scale of spring balance?
Answer
The piece of the wood will float on water and while floating, apparent weight is zero. Hence, the reading on the scale of spring balance will be zero.
Question 3How 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 ?
Question
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 ?
Answer
Question 4A 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?
Question
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?
Answer
When a body floats in a liquid then the weight of the floating body is equal to the upthrust.
Question 5What can you say about the average density of a ship floating on water in relation to the density of water?
Question
What can you say about the average density of a ship floating on water in relation to the density of water?
Answer
According to law of flotation, a body will float in a fluid if it has less density than the fluid. So, in order for the ship to float, its average density must be less than the density of water.
Question 6Two identical pieces, one of ice (density = 900 kg m−3) and other of wood (density = 300 kg m−3) float on water.
Question
(a) Which of the two will have more volume submerged inside water?
(b) Which of the two will experience more upthrust due to water?
Answer
(a) Ice will have more volume submerged inside water, because density of ice is more than the density of wood and we know that the body with higher density will have more volume submerged in water.
(b) Ice will have more volume submerged inside water and hence it will experience greater upthrust than the piece of wood. This is so because the upthrust is always equal to the volume of water displaced by the submerged part of the body and ice will displace more water than the piece of wood.
Question 7A piece of ice floating in a glass of water melts, but the level of water in glass does not change. Give reason.
Question
A piece of ice floating in a glass of water melts, but the level of water in glass does not change. Give reason.
[Hint: Ice contracts on melting.]
Answer
When a floating piece of ice melts into water, it contracts by the volume equal to the volume of ice piece above the water surface while floating on it. Hence, the level of water does not change when the ice floating on it melts.
Question 8A 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 equil…
Question
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.
Answer
The three forces that keep the buoy in equilibrium are —
Exercise 5(C) — Short Answer Type
11 solved questions
Question 1A solid iron ball of mass 500 g is dropped in mercury contained in a beaker. (a) Will the ball float or sink? Give reason. (b) What will be the apparent…
Question
A solid iron ball of mass 500 g 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 ball? Give reason.
Answer
(a) When a solid iron ball of mass 500 g is dropped in mercury contained in a beaker, the ball will float because the density of iron ball is less than the density of mercury.
(b) The apparent weight of the ball is zero because while floating upthrust is equal to the weight of the body.
Question 2Explain why an iron nail floats on mercury, but it sinks in water.
Question
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]
Answer
Iron nail floats on mercury because the density of iron is less than that of mercury but it sinks in water because the density of iron is more than the density of water.
Question 3A 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…
Question
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.
Answer
(a) When a homogenous block floats on water with its body partly immersed then centre of buoyancy B will lie vertically below centre of gravity, G.
(b) When a homogenous block floats on water with its body completely immersed then centre of buoyancy B will coincide with centre of gravity, G.
Question 4Be;pw figure shows the same block of wood floating in three different liquids A, B and C of densities ρ1, ρ2 and ρ3 respectively. Which liquid has the h…
Question
Be;pw figure shows the same block of wood floating in three different liquids A, B and C of densities ρ1, ρ2 and ρ3 respectively. Which liquid has the highest density? Give reason for your answer.
Answer
The liquid C has highest density.
The upthrust on the body by each liquid is the same and it is equal to the weight of body.
For liquid C, since volume submerged is least, so density ρ3 must be maximum.
Question 5What is center of buoyancy? State its position for a floating body with respect to the centre of gravity of body.
Question
What is center of buoyancy? State its position for a floating body with respect to the centre of gravity of body.
Answer
Centre of buoyancy B, is the centre of gravity of the displaced liquid.
The centre of buoyancy B, and centre of gravity G, will coincide if the body is fully immersed in the liquid.
In the case when the body is partially above and partially below the surface of liquid, the centre of buoyancy B is vertically below the centre of gravity G.
Question 6A 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 jar is…
Question
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 jar is pumped out? Explain your answer.
Answer
When air from jar is pumped out the balloon will sink.
As air from jar is pumped out, the density of air in jar decreases, so upthrust on balloon decreases, hence the weight of balloon exceeds the upthrust on it and the balloon sinks.
Question 7A block of wood is so loaded that it just floats in water at room temperature. What change will occur in the state of floatation, if
Question
A block of wood is so loaded that it just floats in 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?
Answer
(a) The block floats with some part outside water when salt is added to the water.
On adding some salt to water, the density of water increases, so upthrust on block of wood increases and hence the block rises up till the weight of salty water displaced by the submerged part of the block becomes equal to the weight of block.
(b) When the water is heated, the block sinks.
On heating the water, the density of water decreases, so upthrust on block decreases and weight of block exceeds the upthrust due to which it sinks.
Question 8Why is floating ice less submerged in brine than in water?
Question
Why is floating ice less submerged in brine than in water?
Answer
Floating ice is less submerged in brine than in water because the density of brine is more than the density of water.
Question 9A man first swims in sea water and then in river water.
Question
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?
Answer
(i) In each case the weight of water displaced will be equal to the weight of the man.
Hence, the ratio weights of sea water and river water displaced by him will be 1:1.
(ii) The man finds it easier to swim in sea water because the density of sea water is more than that of the river water, so his weight is balanced in sea water with his less part submerged inside it.
Question 10An iron nail sinks in water while an iron ship floats on water. Explain the reason.
Question
An iron nail sinks in water while an iron ship floats on water. Explain the reason.
Answer
An iron nail sinks in water because the density of iron is greater than the density of water, so the weight of the nail is more than the upthrust of water on it.
On the other hand, the ship is hollow and the empty space in it contains air which makes it volume large and average density less than that of water. Therefore, even with a small portion of ship submerged in water, the weight of water displaced by the submerged part of ship becomes equal to the total weight of ship and therefore, it floats.
Question 11A loaded cargo ship sails from sea water to river water. State and explain your observation.
Question
A loaded cargo ship sails from sea water to river water. State and explain your observation.
Answer
The ship begins to submerge more as it sails from sea water to river water.
The water of a river is of low density than that of a sea. Therefore, when a loaded cargo ship sails from sea water to river water, it sinks further. The reason is that according to the law of floatation, to balance the weight of ship, a greater volume of water is required to be displaced in water of lower density in river.
Exercise 5(C) — Long Answer Type
9 solved questions
Question 1A body is held immersed in a liquid. (i) Name the two forces acting on body and draw a diagram to show these forces. (ii) State how do the magnitudes of…
Question
A body is held immersed in a liquid. (i) Name the two forces acting on 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 liquid when it is released. (iii) What is the net force on body if it (a) sinks, (b) floats?
Answer
(i) The two forces that act on the body immersed in liquid are —
The weight W of the body acting vertically downwards, through the centre of gravity G of the body. This force has a tendency to sink the body.
The upthrust FB of the liquid acting vertically upwards, through the centre of buoyancy B i.e., the centre of gravity of the displaced liquid. This force has a tendency to make the body float.
(ii) Depending upon whether the maximum upthrust FB is less than, equal to or greater than the weight W, the body will either sink or float in liquid.
When W > FB i.e., the weight of the body is greater than the weight of the displaced liquid then the body will sink.
When W = FB i.e., the weight of the body is equal to the weight of the displaced liquid then the body will float just below the surface of liquid.
When W < FB i.e., the weight of the body is less than the weight of the displaced liquid the body will float partially submerged in the liquid. Only that much portion of the body gets submerged by which the weight of displaced liquid becomes equal to the weight of the body.
(iii) The net force on the body if it sinks/floats is as follows:
In the case when the body sinks, the net force acting on the body is the weight of the body itself.
In the case when the body floats, the net force acting on the body is the upthrust due to the liquid.
Question 2Draw 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.…
Question
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?
Answer
Below diagram shows the forces acting on a body floating in water with its some part submerged:
The forces acting on the body are —
(i) The weight W of body acting vertically downwards, through the centre of gravity G of the body. This force has a tendency to sink the body.
(ii) The upthrust FB of the liquid acting vertically upwards, through the centre of buoyancy B i.e., the centre of gravity of the displaced liquid. This force has a tendency to make the body float.
The weight of the water displaced by the floating body is equal to the weight of the floating body.
Question 3A body of volume V and density ρS, floats with volume v inside a liquid of density ρL. Show that v
Question
A body of volume V and density ρS, floats with volume v inside a liquid of density ρL. Show that
v
V
v
ρ
s
.
Answer
Given,
Volume of body submerged in liquid = v
Density of body = ρS
Density of liquid = ρL
Let weight of the body be W.
Weight of liquid displaced by the body will be equal to upthrust. Let it be FB.
From principle of floatation,
v
V
v
ρ
s
Hence proved.
Question 4(a)Explain the following:
Question
Explain the following:
Icebergs floating in sea are dangerous for ships.
Answer
Icebergs being lighter than water, float on water with their major part (nearly 90%) inside water and only a small portion (say 10%) outside water. Since, the portion of iceberg inside water surface depends on the density of sea water, therefore, for the driver of ship, it becomes difficult to estimate the size of iceberg. Thus, an iceberg is very dangerous for a ship as it may collide with the ship and cause damage.
Question 4(b)Explain the following:
Question
Explain the following:
An egg sinks in fresh water, but floats in a strong salt solution.
Answer
A strong salt solution is denser than fresh water (i.e. density of strong salt solution is more than that of fresh water), hence it will exert more upthrust on the egg that balances the weight of the egg. Therefore, the egg floats in strong salt solution and sinks in fresh water.
Question 4(c)Explain the following:
Question
Explain the following:
A toy balloon filled with hydrogen rises to the ceiling, but if filled with carbon dioxide sinks to the floor.
Answer
When a light gas like hydrogen (density much less than that of air) is filled in a balloon, the weight of air displaced by the inflated balloon (i.e., upthrust) becomes more than weight of the gas filled and it rises up.
However, reverse happens when the balloon is filled with a heavier gas like carbon dioxide (i.e., the weight of air displaced by the inflated balloon (i.e., upthrust) becomes less than weight of the gas filled and hence, the balloon sinks to the bottom.)
Question 4(d)Explain the following:
Question
Explain the following:
As a ship in harbor is being unloaded, it slowly rises higher in water.
Answer
As a ship in harbour is being unloaded, it slowly rises higher in water because the weight of the ship decreases and it displaces less water and therefore, the ship rises in water till the weight of water displaced balances the weight of unloaded ship.
Question 4(e)Explain the following:
Question
Explain the following:
A balloon filled with hydrogen rises to a certain height and then stops rising further.
Answer
A balloon filled with hydrogen rises to a certain height and then stops rising further, because the density of air decreases with altitude. Therefore, as the balloon gradually goes up, the weight of the displaced air (i.e., upthrust) decreases. It keeps on rising as long as the upthrust on it exceeds its weight. When upthrust becomes equal to its weight, it stops rising further.
Question 4(f)Explain the following:
Question
Explain the following:
A ship submerges more as it sails from sea water to river water.
Answer
The ship begins to submerge more as it sails from sea water to river water. The water of river is of low density than that of a sea. Therefore, when a loaded cargo ship sails from sea water to river water, it sinks further. The reason is that according to the law of floatation, to balance the weight of ship, a greater volume of water is required to be displaced in water of lower density i.e., river.
Exercise 5(C) — Numericals
9 solved questions
Question 1A rubber ball floats on water with its 1/3rd volume outside water. What is the density of rubber?
Question
A rubber ball floats on water with its 1/3rd volume outside water. What is the density of rubber?
Answer
Let,
ρ = density of the rubber ball
Given,
1
3
1
rd of V is outside water
Therefore, volume inside water (V')
1
3
1
V
V
By the principle of flotation,
And
2
3
2
V × 1000 × g
Therefore,
2000
3
2000
Question 2A block of wood of mass 24 kg floats on water. The volume of wood is 0.032 m3.
Question
A block of wood of mass 24 kg floats on water. The volume of wood is 0.032 m3.
Find —
(a) the volume of block below the surface of water,
(b) the density of wood.
Answer
(a) Given,
Volume = 0.032 m3
Upthrust = Volume of block below the water × density of liquid × acceleration due to gravity
Hence,
v=
1000
24
3
(b) By the principle of floatation,
Density of water
Density of wood
And
Substituting the values in the formula we get,
1000
Density of wood
0.032
0.024
=7.5×10
2
kg m
−3
Question 3A wooden cube of side 10 cm has mass 700 g. What part of it remains above the water surface while floating vertically on the water surface?
Question
A wooden cube of side 10 cm has mass 700 g. What part of it remains above the water surface while floating vertically on the water surface?
Answer
Given,
Hence,
1000
700
−3
By the principle of floatation,
Density of water
Density of wood
1
0.7
Thus,
Height of wooden cube = 10 cm
Part of woden cube which is submerged = 10 × 0.7 = 7 cm
Therefore, part above water = 10 − 7 = 3 cm
Hence, 3 cm of height of wooden cube remains above water while floating.
Question 4A piece of wax floats on brine. What fractions of its volume is immersed?
Question
A piece of wax floats on brine. What fractions of its volume is immersed?
Answer
Given,
Density of brine = 1.1 g cm−3
By the principle of floatation,
Density of brine
Density of wax
Total volume
Volume of immersed part
1.1
0.95
Hence, the piece of wax floats with 0.86th part of its volume immersed in brine surface.
Question 5If the density of ice is 0.9 g cm−3, what portion of an iceberg will remain below the surface of water in a sea? (Density of sea water = 1.1 g cm−3)
Question
Answer
Given,
Density of sea water = 1.1 g cm−3
By the principle of floatation,
Density of sea water
Density of ice
Total volume
Volume of immersed part
1.1
0.9
11
9
th of total volume (or 0.818th) part.
Question 6A piece of wood of uniform cross section and height 15 cm floats vertically with its height 10 cm in water and 12 cm in spirit. Find the density of (i)…
Question
A piece of wood of uniform cross section and height 15 cm floats vertically with its height 10 cm in water and 12 cm in spirit. Find the density of (i) wood and (ii) spirit.
Answer
Given,
Height of the wood in water = 10 cm
Height of the wood in spirit = 12 cm
As the block of wood is of uniform cross-sectional area, the height of the block is proportional to the volume
By the principle of floatation,
Density of water
Density of wood
15
10
1
Density of wood
15
10
−3
In the case of spirit, substituting the values in the formula above, we get,
Density of spirit
Density of wood
15
12
Density of spirit
0.667
12
15
−3
Question 7A wooden block floats in water with two-third of its volume submerged.
Question
A wooden block floats in water with two-third of its volume submerged.
(a) Calculate the density of wood.
(b) When the same block is placed in oil, three-quarter of its volume is immersed in oil. Calculate the density of oil.
Answer
(a) Let volume of wooden block be V.
Given,
Density of water = 1000 kg m−3
By the principle of floatation,
Density of water
Density of wood
V
3
2
V
1000
Density of wood
3
2
=666.6666 kg m
−3
≈667 kg m
−3
Hence, the density of wood is approximately 667 kg m−3.
V
By the principle of floatation,
Density of oil
Density of wood
V
4
3
V
Density of oil
667
3
4
=889.33 kg m
−3
≈889 kg m
−3
Hence, the density of oil is approximately 889 kg m−3.
Question 8The density of ice is 0.92 g cm−3 and that of sea water is 1.025 g cm−3. Find the total volume of an iceberg which floats with its volume 800 cm3 above…
Question
The density of ice is 0.92 g cm−3 and that of sea water is 1.025 g cm−3. Find the total volume of an iceberg which floats with its volume 800 cm3 above water.
Answer
Given,
Density of sea water = 1.025 g cm−3
Volume of iceberg above sea water = 800 cm3
Let total volume of iceberg be V cm3
By the principle of floatation,
Density of water
Density of ice
V
(V−800)
1.025
0.92
⇒1.025V−820=0.92V
⇒1.025V−0.92V=820
⇒0.105V=820
⇒V=
0.105
820
3
Question 9A weather forecasting plastic balloon of volume 15 m3 contains hydrogen of density 0.09 kg m−3. The volume of an equipment carried by the balloon is neg…
Question
A weather forecasting plastic balloon of volume 15 m3 contains hydrogen of density 0.09 kg m−3. The volume of an equipment carried by the balloon is negligible compared to its own volume. The mass of empty balloon alone is 7.15 kg. The balloon is floating in air of density 1.3 kg m−3. Calculate : (i) the mass of hydrogen in the balloon, (ii) the mass of hydrogen and balloon, (iii) the total mass of hydrogen, balloon and equipment if the mass of equipment is × kg, (iv) the mass of air displaced by balloon and (v) the mass of equipment using the law of floatation.
Answer
Given,
Density of hydrogen = 0.09 kg m−3
Mass of the unfilled balloon = 7.15 kg
Density of air = 1.3 kg m−3
(i) As we know,
Substituting the value in the formula we get,
(iii) Given,
(v) By law of floatation,
Substituting the values in the formula we get,
19.5
Exercise 5(C) — Assertion Reason Type
0 solved questions
Exercise 5(C) — Case Study
2 solved questions
Question 1Three solid objects A, B, and C have the same volume but different masses. They are released gently, one by one, into tanks containing three different l…
Question
Three solid objects A, B, and C have the same volume but different masses. They are released gently, one by one, into tanks containing three different liquids:
L1 (water), L2 (kerosene) and L3 (corrcentrated salt solution).
The observations made are as follows:
(a) Arrange the liquids in increasing order of density, giving reasons.
(b) Identify the condition of flotation of object B in liquid L3. What inference can be drawn about the densities of the object and liquid?
(c) "As object C floats in all three liquids, the upthrust acting on it is the same in all three cases." Is this statement correct? Explain.
(d) If object A is heated (without any change in mass) and then placed in L1, what change, if any, will occur in its floating level?
(e) Two similar ships made of the same material float in fresh water and sea water respectively. Which ship displaces more water and why?
Answer
(a) From the observations :
Object A sinks in L2 but floats in L1 and L3, which means L2 has the least density i.e., ρL2 < ρA < ρL1, ρL3.
Object B sinks in L1 but floats (fully submerged) in L3, indicating that L3 has the highest density i.e., ρL1 < ρB < ρL3.
Since L1 lies between these two cases, its density is intermediate.
Hence, the increasing order of density is ρL2 (kerosene) < ρL1 (water) < ρL3 (concentrated salt solution).
(b) The condition of flotation is:
W = weight of body acting vertically downwards
FB = Maximum upthrust that can act on the body
As object B floats fully submerged in L3, hence, we can say that density of object B is equal density of liquid L3
(c) The statement is correct because although object C floats in all three liquids, the upthrust acting on it is equal to its weight in each case, but the volume of liquid displaced is different depending on the density of the liquid.
In denser liquids, a smaller volume is displaced, while in less dense liquids, a larger volume is displaced so, while upthrust equals weight in all cases, the surrounding conditions like submerged volume differ.
(d) When object A is heated, its volume increases while its mass remains the same, leading to a decrease in its density so as a result, it will displace same amount of liquid to balance its weight but due to its larger volume it will be submerged less and hence will float higher in liquid L1.
(e) The ship floating in fresh water displaces more volume because fresh water has lower density compared to sea water so to balance its weight, the ship must displace a larger volume of fresh water, whereas in denser sea water, a smaller volume is sufficient to provide the required upthrust.
Question 2The figure shows three identical solid cubes P, Q, and R of the same volume and material placed in three different liquids in identical vessels.
Question
The figure shows three identical solid cubes P, Q, and R of the same volume and material placed in three different liquids in identical vessels.
Answer the following :
(a) Arrange the liquids in increasing order of density.
(b) Identify the condition of flotation of cube R in liquid B. What information does this give about the densities of cube R and liquid B?
(c) Compare the upthrust acting on cubes P, Q, and R.
(d) If cube P is placed in liquid B, predict whether it will float higher, lower, or remain fully submerged. Give reason.
(e) Which liquid exerts the maximum buoyant force on a cube when it is fully immersed, and why?
Answer
(a) From the figure :
Cube P is half submerged in liquid A,
Cube Q is 3/4 submerged in liquid C, and
Cube R is fully submerged in liquid B.
For identical objects, a greater submerged portion indicates a lower density of the liquid. Thus, liquid B (fully submerged) has the least density, liquid C (3/4 submerged) has intermediate density and liquid A (half submerged) has the highest density.
Hence, increasing order of density is ρB < ρC < ρA.
(b) The condition of flotation is:
W = weight of cube R acting vertically downwards
FB = Maximum upthrust that can act on cube R
As cube R floats fully submerged in liquid B, hence, we can say that density of cube R is equal density of liquid B.
(c) All three cubes are identical and floating, so the upthrust acting on each cube is equal to its weight and since their weights are the same, the upthrust on P, Q, and R is equal, even though the submerged volumes differ.
(d) We know that Cube R floats fully submerged in liquid B. As all the cubes are identical, so cube P when placed in liquid B will also float fully submerged.
Therefore, cube P will remain fully submerged in liquid B.
(e) Liquid A exerts the maximum buoyant force on a cube when it is fully immersed.
Reason / Explanation
: When a cube is fully immersed, the buoyant force depends on the density of the liquid and the volume displaced and since all cubes have the same volume, the liquid with the highest density will exert the maximum buoyant force, because buoyant force is directly proportional to the density of the liquid.
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