Upthrust Class 9 ICSE — Physics Chapter 5

Upthrust Class 9 ICSE Physics Chapter 5 explains why some things float and others sink. The chapter defines upthrust and buoyancy, proves that upthrust equals the weight of the displaced liquid, and states Archimedes’ principle. It then builds density and relative density, the principle of floatation, and real applications such as ships, submarines, icebergs and balloons. The official CISCE website, cisce.org, publishes the Class 9 Physics syllabus this chapter follows.

Download Upthrust in Fluids Archimedes Principle and Floatation Class 9 ICSE Physics Chapter 5 PDF

Download the Upthrust in Fluids Archimedes Principle and Floatation Class 9 ICSE Physics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 21 pages, 14 sections, 83 questions.

What is inside Chapter 5

21 pages · 14 sections · 4 worked examples · 83 exercise questions

• EXERCISE 5(A): 26 questions
• Multiple choice type :: 12 questions
• EXERCISE 5(B): 15 questions
• Multiple choice type :: 18 questions
• Multiple choice type :: 12 questions

5.1 BUOYANCY AND UPTHRUST

When a body is partly or fully immersed in a liquid, the liquid pushes it upwards. That upward force is the upthrust, also called the buoyant force, written F_B. Buoyancy is the property of a liquid that makes it exert this upward force. Since upthrust is a force, its unit is newton (N) or kgf.

You can feel upthrust directly. Push an empty, sealed can into a tub of water. The deeper it goes, the more force you need. Release it, and it bounces back to the surface. A cork behaves the same way, floating with about \frac{2}{5} of its volume below the surface.

Two forces act on the can or cork: its weight W downward and the upthrust F_B upward. The upthrust grows as more volume submerges and reaches its maximum F_B' when the body is fully immersed. If F_B' \geq W, the body floats. If F_B' \lt W, it sinks with acceleration a = \frac{W - F_B'}{m}. Gases exert upthrust too, which is why a hydrogen balloon rises.

5.2 CHARACTERISTIC PROPERTIES OF UPTHRUST

Upthrust has three characteristic properties. First, the larger the submerged volume, the greater the upthrust. Second, for the same submerged volume, the denser the fluid, the greater the upthrust. Third, upthrust acts upward at the centre of buoyancy, which is the centre of gravity of the displaced liquid.

The first property explains a classic demonstration. A bunch of feathers and a pebble of the same mass fall in air; the pebble lands first because its smaller volume meets less air upthrust. In vacuum, both fall together.

The second property shows when identical corks float in water and glycerine, the cork in denser glycerine sits higher. The third property matters for floating bodies: when a body floats partly submerged, the centre of buoyancy lies below the body’s centre of gravity.

5.3 REASON FOR UPTHRUST

Upthrust comes from the way liquid pressure works. At any point in a liquid, pressure acts equally in all directions, and it increases with depth. For a block of cross-section area A, the lower face sits at a greater depth than the upper face.

So the pressure P_2 on the lower face exceeds P_1 on the upper face. That pressure difference creates a net upward force (P_2 - P_1)A, which is the upthrust. The thrusts on the side faces cancel because they are equal and opposite at the same depth.

This is the same liquid pressure behaviour studied in Chapter 4 of the Class 9 Physics book, which covers pressure in fluids and atmospheric pressure. One warning: a thin lamina feels almost equal pressure on both faces, so upthrust becomes negligible and the sheet sinks.

5.4 UPTHRUST IS EQUAL TO THE WEIGHT OF DISPLACED LIQUID (Mathematical proof)

The proof uses a cylindrical body PQRS of cross-sectional area A immersed in a liquid of density \rho. Let the upper face sit at depth h_1 and the lower face at depth h_2. Pressure on the upper face is P_1 = h_1 \rho g, so the downward thrust is F_1 = h_1 \rho g A.

Similarly, P_2 = h_2 \rho g and the upward thrust is F_2 = h_2 \rho g A. Since h_2 \gt h_1, the upward thrust wins.

F_B = F_2 - F_1 = A(h_2 - h_1)\rho g = V\rho g

Here A(h_2 - h_1) is the volume V of the submerged body. The product V\rho is the mass of liquid the body displaces, so V\rho g is its weight. The result holds for any shape. Upthrust therefore depends on only two factors: the submerged volume and the liquid’s density. This is why a bucket of water feels light while it is still under water and heavy the moment it breaks the surface.

5.5 ARCHIMEDES’ PRINCIPLE

When a body enters a liquid, it displaces liquid equal to the volume of its submerged part. The displaced liquid was pushing upwards before the body arrived; now that push acts on the body.

Archimedes’ principle states that a body immersed partially or completely in a liquid experiences an upthrust equal to the weight of the liquid it displaces. Because of this upthrust, the body appears lighter in the liquid. The apparent loss in weight equals the upthrust. The principle applies to gases as well as liquids.

5.6 EXPERIMENTAL VERIFICATION OF ARCHIMEDES’ PRINCIPLE

Two classic experiments verify the principle. In the first, hang a solid cylinder below a hollow cylinder of the same volume from a physical balance and balance the beam with weights. Immerse the solid cylinder in a beaker of water without touching the sides. The beam tilts because the solid loses weight.

Now pour water into the hollow cylinder until it is full. The beam balances again. The hollow cylinder holds exactly the weight of water the solid displaced, which proves upthrust equals that weight.

The second experiment uses a eureka can and a spring balance. Suppose a stone weighs 250 gf in air and 160 gf fully immersed in water. Its loss in weight is 90 gf. The displaced water collected from the can measures 90 cm³, and since water has density 1 g cm⁻³, the weight of displaced water is 90 gf. The two match, confirming Archimedes’ principle.

5.7 SOLID BODIES WITH DENSITY (rho) GREATER THAN DENSITY OF LIQUID (rho_L) SINK WHILE WITH DENSITY (rho) LESS THAN DENSITY OF LIQUID (rho_L) FLOAT

Compare the two forces for a body of volume V and density \rho fully immersed in a liquid of density \rho_L. The weight is W = V\rho g and the maximum upthrust is F_B' = V\rho_L g. Volume and g cancel out of the comparison, so density alone decides the outcome.

If \rho \gt \rho_L, the body sinks. If \rho = \rho_L, it floats with its whole volume submerged. If \rho \lt \rho_L, it floats partly submerged, with just enough volume inside the liquid for the upthrust to balance its weight. This is why an iron nail sinks but a cork of the same mass floats.

A hollow body, like an empty tin can or an iron ship, floats because its average density is low. Average density is the total mass of material plus enclosed air divided by total volume. A quick mnemonic: dense dives, light lifts — compare the body’s density with the liquid’s.

5.8 DENSITY

Density is mass per unit volume: \rho = \frac{M}{V}. It is a scalar quantity. In S.I. units it is kg m⁻³, and in C.G.S. units g cm⁻³. The conversion is 1\ \text{g cm}^{-3} = 1000\ \text{kg m}^{-3}.

Most substances expand when heated, so their density falls. Water is the exception. It contracts on cooling only down to 4°C, then expands down to 0°C. So water has its maximum density, 1\ \text{g cm}^{-3} or 1000\ \text{kg m}^{-3}, at 4°C. This chapter sits inside the wider Class 9 Physics collection.

5.9 RELATIVE DENSITY

Relative density compares a substance with water at 4°C. It is the ratio of the density of the substance to the density of water at 4°C. For equal volumes, it is also the ratio of the mass of the substance to the mass of that same volume of water.

Relative density has no unit, because a ratio of two densities cancels the units. It is a pure ratio and a scalar. The conversion rules are simple: density in g cm⁻³ equals the R.D. numerically, and density in kg m⁻³ equals R.D. × 1000.

The textbook’s table of common substances lists cork at R.D. 0.24, sea water at 1.02, glycerine at 1.26 and mercury at 13.6. A common slip is to confuse density with relative density: density has units, relative density does not.

5.10 DETERMINATION OF RELATIVE DENSITY OF A SOLID SUBSTANCE BY ARCHIMEDES’ PRINCIPLE

To find the relative density of a solid, weigh it in air and then weigh it fully immersed in water. If W_1 is the weight in air and W_2 the weight in water, then

\text{R.D.} = \frac{W_1}{W_1 - W_2}

The denominator is the loss in weight, which equals the weight of displaced water. Procedure: suspend the solid from the left pan of a physical balance and weigh it in air. Place a beaker of water on a wooden bridge over the pan so the bridge does not touch the pan. Immerse the solid completely without touching the beaker’s walls or bottom, and record the new weight.

Worked pattern: a stone weighs 150 gf in air and 95 gf in water. The loss is 55 gf, so the upthrust is 55 gf. The volume of the stone is 55 cm³, and its relative density is \frac{150}{55} = 2.73. If the solid dissolves in water, use a liquid of known R.D. in which it is insoluble, then multiply the result by that liquid’s R.D.

5.11 DETERMINATION OF RELATIVE DENSITY OF A LIQUID BY ARCHMEDES’ PRINCIPLE

The same idea finds the relative density of a liquid. Weigh a body that is denser than both the liquid and water, and insoluble in both. Let W_1 be its weight in air, W_2 its weight in the liquid, and W_3 its weight in water. Then

\text{R.D. of liquid} = \frac{W_1 - W_2}{W_1 - W_3}

The same body displaces its own volume in each fluid, so the displaced volumes are equal. That is why the weights of displaced liquid and water can be compared directly.

Worked pattern: a body weighs 100 gf in air, 82 gf in a liquid, and 80 gf in water. Then

\text{R.D.} = \frac{100 - 82}{100 - 80} = \frac{18}{20} = 0.9

The liquid is slightly less dense than water.

5.12 PRINCIPLE OF FLOATATION

For a body in a liquid, weight W acts downward through the centre of gravity, and upthrust F_B acts upward through the centre of buoyancy. Three cases follow from comparing W with the maximum upthrust F_B'.

When W \gt F_B', the body sinks with apparent weight W - F_B'. When W = F_B', it floats just below the surface with zero apparent weight. When W \lt F_B', it floats partly submerged, and the submerged part displaces liquid whose weight equals the body’s weight.

So the principle of floatation states: the weight of a floating body equals the weight of the liquid displaced by its submerged part. For every floating body, the apparent weight is zero.

5.13 RELATION BETWEEN VOLUME OF SUBMERGED PART OF A FLOATING BODY, THE DENSITIES OF LIQUID AND

Let a body of total volume V and density \rho_s float with volume v submerged in a liquid of density \rho_L. For floatation, weight equals upthrust:

V\rho_s g = v\rho_L g

Cancelling g gives the key ratio

\frac{v}{V} = \frac{\rho_s}{\rho_L}

The fraction submerged is just the ratio of densities, so it has no unit. The textbook’s examples show a cork with \frac{3}{4} of its volume under water and an ice cube with 90% submerged.

Worked pattern: a wooden block of density 600\ \text{kg m}^{-3} floats in oil of density 800\ \text{kg m}^{-3}. Then \frac{v}{V} = \frac{600}{800} = 0.75, so three-quarters of the block stays submerged.

5.14 APPLICATIONS OF THE PRINCIPLE OF FLOATATION

The principle of floatation explains many everyday situations. Each application uses the same idea: a body floats when the weight of displaced liquid equals its own weight.

• Iron ship: the hollow hull gives a large volume and low average density, so it floats. The Plimsoll line marks the safe loading limit in water of density 10^3\ \text{kg m}^{-3}. A ship sinks deeper in river water, and unloaded ships carry ballast to lower the centre of gravity.
• Human body: lungs filled with air bring the average density near 1\ \text{g cm}^{-3}, so a swimmer floats. Sea water is denser than fresh water, so swimming in the sea is easier.
• Submarine: ballast tanks fill with water to dive; compressed air forces the water out to rise.
• Iceberg: about 91.7% of its volume is below fresh water and 89.3% below sea water. Melting floating ice does not change the water level.
• Fish: the swim bladder fills with gas to rise and empties to sink.
• Balloon: hydrogen or helium gives an upthrust greater than the weight, so the balloon rises until upthrust equals weight.

What to practise from Upthrust Class 9 ICSE

The exercise blocks in this chapter follow the order of the sections. Work through them in sequence, and use the mapping below to connect each block to the ideas it tests.

• Exercise 5(A): 26 questions covering upthrust, buoyancy and Archimedes’ principle (sections 5.1 to 5.7).
• Multiple choice questions after Exercise 5(A): 12 questions.
• Exercise 5(B): 15 questions on density and relative density (sections 5.8 to 5.11).
• Multiple choice questions after Exercise 5(B): 18 questions.
• Final multiple choice set: 12 questions on the principle of floatation and its applications (sections 5.12 to 5.14).

While practising, watch three common slips. Do not confuse density with relative density — one has units, the other does not. Remember that upthrust depends on the submerged volume and the liquid’s density, not on the total mass of the body. And when a body floats, its apparent weight is zero, not small. For more chapters, browse the Class 9 Physics collection.

Upthrust Class 9 ICSE frequently asked questions

What is upthrust in fluids for Class 9 ICSE?

Upthrust is the upward force a fluid exerts on a body that is partly or fully immersed in it. It is also called the buoyant force. Its magnitude equals the weight of the displaced liquid, and its unit is newton or kgf.

Why does an iron nail sink in water but an iron ship floats?

The nail has the full density of iron, which is greater than water’s density, so its weight exceeds the maximum upthrust. The ship is hollow, so its average density — mass of iron plus enclosed air divided by total volume — is less than water’s density. A small submerged volume then displaces enough water to balance the ship’s weight.

How are density and relative density different in Class 9 ICSE Physics?

Density is mass per unit volume and has units such as g cm⁻³ or kg m⁻³. Relative density is the ratio of a substance’s density to the density of water at 4°C, so it has no unit. Numerically, density in g cm⁻³ equals the relative density.

How do you find the relative density of a solid using Archimedes’ principle in this ICSE chapter?

Weigh the solid in air (W_1) and fully immersed in water (W_2). The relative density is W_1 \div (W_1 - W_2). The denominator is the loss in weight, which equals the weight of displaced water. For a solid soluble in water, use a liquid of known relative density and multiply the result by it.

Why does an iceberg float with most of its volume under water in Class 9 ICSE Physics?

Because ice is less dense than water, the fraction submerged equals the ratio of densities. Ice at 0.917 g cm⁻³ in water at 1 g cm⁻³ has about 91.7% of its volume below the surface. Only the remaining 8.3% is visible above water.

Reference: ICSE Class 9 Physics textbook material, chapter 5: Upthrust in Fluids Archimedes Principle and Floatation — CISCE-aligned.

More from this book

• Chapter 1: Measurements and Experimentation
• Chapter 2: Motion in One Dimension
• Chapter 3: Laws of Motion
• Chapter 4: Pressure in Fluids and Atmospheric Pressure
• Chapter 6: Heat and Energy
• Chapter 7: Reflection of Light
• Chapter 8: Propagation of Sound Waves
• Chapter 9: Current Electricity
• Chapter 10: Magnetism