Upthrust in Fluids and Archimedes' Principle | Class 9 ICSE Physics- Analytical based

ICSE Physics | Class 9

The Mystery of Floating Objects!

Upthrust in Fluids and Archimedes' Principle

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Can a heavy iron ship float while a tiny iron nail sinks?

Can water make a heavy stone appear lighter?

Discover the answers through experiments, analytical questions and real-life challenges.

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1. Learning Objectives

By the end of this lesson, you will be able to:

• Define upthrust and buoyant force.
• Explain the origin and direction of upthrust in a fluid.
• State Archimedes' principle.
• Calculate upthrust using the volume and density of a displaced fluid.
• Explain apparent loss of weight in a liquid.
• Distinguish between actual weight and apparent weight.
• Analyse the conditions under which an object floats or sinks.
• Apply the principle of flotation to everyday situations.
• Solve numerical problems involving upthrust and displaced liquids.
• Develop scientific reasoning through competency-based questions.

2. A Small Story: The Stone That Became Lighter!

One afternoon, Aarav visited a science laboratory with his classmates.

His teacher suspended a heavy stone from a spring balance. The balance showed a reading of 10 N.

Then she slowly lowered the stone into a beaker of water without allowing it to touch the bottom.

Something surprising happened. The reading decreased to 7 N!

"Ma'am, has the stone lost some of its weight?" Aarav asked.

"No," replied the teacher. "Its weight due to gravity has not changed. Water is exerting an upward force on it."

The teacher explained that this upward force is called upthrust. She also showed the class how the weight of the displaced water could be used to calculate it.

Aarav then understood how the same principle explains floating ships, submarines and hydrometers.

The discovery: An observation becomes a scientific explanation when we connect it to evidence and a physical principle.

Story-Based Questions

1. Why did the spring balance reading decrease?
2. Did the actual weight of the stone change?
3. Calculate the upthrust acting on the stone.
4. Which scientific principle explains the relationship between upthrust and displaced water?

Reveal the answers

1. Water exerted an upward force on the immersed stone.

2. No. Its actual weight remained unchanged.

3. Upthrust = 10 − 7 = 3 N.

4. Archimedes' principle.

3. What Is Upthrust?

Upthrust is the upward force exerted by a fluid on a body wholly or partially immersed in it.

A fluid can be a liquid, such as water, or a gas, such as air.

Why Does Upthrust Act?

Pressure in a liquid increases with depth. Therefore, the lower surface of an immersed object generally experiences greater pressure than its upper surface.

The resulting pressure difference produces a net upward force called upthrust.

Important Characteristics

• Upthrust acts vertically upwards.
• It opposes the weight of an object.
• It acts on immersed objects whether they float or sink.
• Its magnitude depends on the density of the fluid and the volume of fluid displaced.
• Its SI unit is the newton (N).

Try This Investigation!

Take a stone, a spring balance and a container of water.

1. Measure the weight of the stone in air.
2. Immerse the stone completely in water.
3. Observe the new spring balance reading.
4. Subtract the immersed reading from the reading in air.

The difference gives the upthrust, assuming the stone does not touch the container and other effects are negligible.

Upthrust = Weight in air − Apparent weight in liquid

4. Archimedes' Principle

Archimedes' principle states:

When a body is wholly or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced by it.

Upthrust = Weight of displaced fluid

Mathematically:

U = ρVg

Where:

• U = upthrust in newtons (N)
• ρ = density of the fluid in kg/m³
• V = volume of fluid displaced in m³
• g = acceleration due to gravity in m/s²

Three Important Ideas

1. An object completely immersed in a fluid displaces a volume of fluid equal to its own volume.

2. A partially immersed object displaces a volume of fluid equal to the volume of its submerged portion.

3. For a floating object at rest, the upthrust equals the weight of the object.

5. Apparent Loss of Weight

When an object is immersed in a liquid, the liquid exerts an upward force on it. The object therefore appears lighter.

Apparent Weight = Actual Weight − Upthrust

Worked Example

A metal block weighs 25 N in air and 18 N when immersed completely in water.

Calculate its upthrust.

Upthrust = 25 − 18

Answer: 7 N

According to Archimedes' principle, the weight of the displaced water is also 7 N.

Remember

The object does not lose mass when immersed in water. Its actual gravitational weight remains unchanged, but its apparent weight decreases because of upthrust.

6. Why Do Objects Float or Sink?

Situation	Scientific Explanation
Object less dense than the fluid	It can float partially submerged.
Object denser than the fluid	It sinks when released under ordinary conditions.
Object has the same average density as the fluid	It can remain suspended when fully immersed and in equilibrium.
Object floating at rest	Upthrust equals the object's weight.

The Iron Ship Mystery

A solid iron nail sinks, but a hollow iron ship floats.

Why?

A ship has a hollow structure containing air. Its average density is sufficiently low for it to displace enough water to balance its weight.

The shape and total volume of the ship allow it to displace a large volume of water before becoming fully submerged.

7. Textbook-Based MCQs

These questions follow the concepts and question patterns in your uploaded ICSE textbook exercise.

1. When an empty can is pushed into water, we feel:

A downward force An upward force No force Only a sideways force

2. An object immersed in a liquid appears to weigh:

More than its actual weight Exactly twice its actual weight Less than its actual weight Zero in every case

3. Which statement about upthrust is correct?

For the same fluid, a smaller displaced volume produces a smaller upthrust. Upthrust always equals the object's mass. Upthrust acts vertically downwards. Upthrust acts only on floating objects.

4. The correct relation for upthrust is:

U = ρ/Vg U = V/ρg U = ρg/V U = ρVg

5. Archimedes' principle applies to:

Solids only Liquids only Gases only Fluids, including liquids and gases

6. A body is completely immersed in a liquid. The volume of liquid displaced is:

Always smaller than the body's volume Equal to the body's volume Always greater than the body's volume Zero

7. A cork floats on water because:

It has no mass Gravity does not act on it Its average density is less than that of water Water exerts no pressure on it

8. An iron nail sinks in water because:

Its density is greater than the density of water Its density is less than the density of water Water has no upthrust Gravity does not act on water

9. Iron and aluminium balls of equal volume are completely immersed in water. Their upthrusts are:

Greater on the iron ball Greater on the aluminium ball Equal Zero on both

10. A body experiences minimum upthrust when immersed in which of these fluids, assuming equal displaced volumes?

Mercury Glycerine Water Turpentine

11. A cork floats at rest on water. The upthrust is:

Greater than its weight Equal to its weight Less than its weight Zero

12. The weight of the liquid displaced by a floating body is:

Equal to the weight of the body Always zero Greater than the body's weight in every case Unrelated to the body's weight

Your Textbook Practice Report

8. Analytical Questions: Think Beyond the Textbook

Question 1: Two Identical Stones

Two identical stones are immersed completely in water. One is placed near the surface and the other at a greater depth.

Will the upthrust on them differ? Explain your reasoning.

Reveal the answer

Assuming water density remains constant and both stones are fully immersed, the upthrusts are equal because both displace equal volumes of water.

Upthrust depends on the weight of displaced fluid, not simply on depth.

Question 2: The Heavier Object

Two objects of different masses have equal volumes. Both are completely immersed in the same liquid.

Which object experiences greater upthrust?

Reveal the answer

Both experience equal upthrust because they displace equal volumes of the same liquid.

The heavier object has greater weight, but that does not mean it experiences greater upthrust.

Question 3: Water or Glycerine?

The same object is completely immersed in water and then in glycerine. Assume glycerine is denser than water.

In which liquid is the apparent weight smaller?

Reveal the answer

In glycerine, because it exerts greater upthrust for the same displaced volume. The greater upthrust produces a smaller apparent weight.

Question 4: A Floating Block

A wooden block floats with 60% of its volume submerged in water.

What can you conclude about its density compared with the density of water?

Reveal the answer

For a floating block:

Density of block ÷ Density of water = Fraction submerged.

Therefore, the density of the block is 0.60 times the density of water.

If water has a density of 1000 kg/m³, the block's density is 600 kg/m³.

Question 5: The Disappearing Weight

A body weighs 40 N in air and 28 N when immersed completely in a liquid.

Calculate the upthrust and state what the result tells you about the weight of the displaced liquid.

Reveal the answer

Upthrust = 40 − 28 = 12 N.

By Archimedes' principle, the weight of the displaced liquid is also 12 N.

Question 6: The Floating Ship

A ship is carrying cargo and floating safely. More cargo is loaded onto it.

Explain why the ship sinks deeper into the water.

Reveal the answer

Additional cargo increases the total weight of the ship. To balance this greater weight, the ship must displace more water, producing greater upthrust.

The ship sinks deeper until the upthrust balances the new total weight, provided it remains within safe loading limits.

9. Competency-Based Case Study: The Spring Balance Investigation

A student performs an experiment using a metal object, a spring balance and a beaker of water.

Observation	Reading
Weight in air	15 N
Apparent weight in water	11 N

Answer the questions

1. Calculate the upthrust.

Show solution

Upthrust = Weight in air − Apparent weight in water

= 15 − 11

Answer: 4 N

2. What is the weight of the displaced water?

Show solution

By Archimedes' principle, the weight of displaced water equals the upthrust.

Answer: 4 N

3. What would happen to the apparent weight if the same object displaced an equal volume of a denser liquid?

Show answer

The apparent weight would be smaller because the denser liquid would exert greater upthrust.

4. Does the object's actual weight change when it is immersed?

Show answer

No. Its actual gravitational weight remains unchanged. The spring balance reading decreases because of upthrust.

10. Numerical Challenge: Apply the Formula

Problem 1

A body of volume 100 cm³ is completely immersed in water. Calculate the upthrust.

Density of water = 1000 kg/m³ and g = 10 m/s².

Reveal the solution

Convert volume into SI units:

100 cm³ = 100 × 10⁻⁶ m³ = 0.0001 m³.

U = ρVg

U = 1000 × 0.0001 × 10

Answer: 1 N

Problem 2

A solid object weighs 50 N in air and 30 N in water. Calculate:

a. Upthrust

b. Weight of displaced water

c. Apparent loss of weight

Reveal the solution

a. Upthrust = 50 − 30 = 20 N

b. Weight of displaced water = 20 N

c. Apparent loss of weight = 50 − 30 = 20 N

Problem 3

A body displaces 0.005 m³ of a liquid of density 800 kg/m³. Calculate the upthrust. Take g = 10 m/s².

Reveal the solution

U = ρVg

U = 800 × 0.005 × 10

Answer: 40 N

Problem 4

A wooden block of volume 0.003 m³ and mass 2 kg is placed in water. Will it float or sink?

Density of water = 1000 kg/m³ and g = 10 m/s².

Reveal the solution

Weight of the block = mg

= 2 × 10 = 20 N.

Maximum upthrust when fully immersed:

U = 1000 × 0.003 × 10 = 30 N.

Since the block's weight is less than the maximum available upthrust, it can float.

At floating equilibrium, it displaces water weighing 20 N.

Volume submerged = 20 ÷ (1000 × 10)

= 0.002 m³.

Answer: It floats with two-thirds of its volume submerged.

11. Thinking-Based MCQs: Challenge Your Brain!

These questions require analysis and application. Read carefully before selecting an answer.

10 questions | 1 mark each

1. An iron sphere and a wooden sphere have equal radii. Both are completely immersed in water. Which statement is correct?

The iron sphere experiences greater upthrust because it is heavier. The wooden sphere experiences greater upthrust because it is lighter. Both experience equal upthrust. Neither experiences upthrust.

2. A metal block is fully immersed in water and then in a denser liquid. What happens to its apparent weight?

It increases. It decreases. It remains exactly the same. It becomes equal to its mass.

3. A body weighs 25 N in air and 17 N in a liquid. The weight of the displaced liquid is:

8 N 17 N 25 N 42 N

4. A body is moved deeper into a liquid but remains completely immersed. If the liquid density is uniform, its upthrust:

Always doubles. Always decreases. Becomes zero. Remains unchanged.

5. A wooden block floats at rest on water. The resultant vertical force on it is:

Equal to its weight. Directed upwards. Zero. Directed downwards.

6. An object floats in water with 40% of its volume submerged. If the density of water is 1000 kg/m³, the object's density is:

400 kg/m³ 600 kg/m³ 1000 kg/m³ 1400 kg/m³

7. More cargo is loaded onto a floating ship. Assuming it remains safe, the ship will:

Displace less water. Sink deeper and displace more water. Experience no change in upthrust. Lose its gravitational weight.

8. An object displaces 0.002 m³ of water. Take water density as 1000 kg/m³ and g = 10 m/s². The upthrust is:

2 N 10 N 200 N 20 N

9. A hollow metal container floats, but begins to sink after water enters through a hole. Why?

The metal loses its density. Gravity suddenly increases. Its total mass increases, so more upthrust is needed to balance its weight. Water stops exerting pressure.

10. A hydrometer is placed in two liquids. In which liquid will it generally float higher?

The denser liquid. The less dense liquid. Both liquids must produce the same depth. Neither liquid.

Your Analytical Thinking Report

12. Values We Learn Through Science

Curiosity

Ask questions about everyday observations instead of accepting them without investigation.

Logical Thinking

Use evidence, measurements and scientific principles to reach conclusions.

Responsibility

Understand why safe loading limits are important for ships and boats.

Care for Nature

Protect rivers, lakes and oceans because healthy aquatic environments support life.

Perseverance

When a numerical problem seems difficult, identify the known quantities, choose the correct formula and solve it step by step.

13. The Final Scientist Challenge

Can You Solve This Without Help?

A metal object weighs 60 N in air. When fully immersed in water, its apparent weight is 45 N.

The density of water is 1000 kg/m³ and g = 10 m/s².

Answer all four questions.

1. Calculate the upthrust.
2. Calculate the weight of water displaced.
3. Calculate the volume of water displaced.
4. Would the same object experience greater or smaller upthrust in a liquid denser than water, assuming it displaces the same volume?

Reveal the complete solution

1. Upthrust

U = 60 − 45 = 15 N.

2. Weight of displaced water

By Archimedes' principle, it is equal to the upthrust.

Answer = 15 N.

3. Volume displaced

U = ρVg

V = U ÷ ρg

V = 15 ÷ (1000 × 10)

Answer = 0.0015 m³, or 1500 cm³.

4. In a denser liquid

The upthrust will be greater because the same displaced volume of a denser liquid has greater weight.

14. Quick Revision

• Upthrust is the upward force exerted by a fluid on an immersed body.
• Upthrust occurs because fluid pressure differs across the body's surfaces.
• Archimedes' principle: Upthrust equals the weight of fluid displaced.
• Upthrust = ρVg.
• Apparent weight = Actual weight − Upthrust.
• For a fully immersed body, displaced fluid volume equals the body's volume.
• A floating object at rest has upthrust equal to its weight.
• A body less dense than a fluid can float partially submerged.
• Objects of equal volume, fully immersed in the same fluid, experience equal upthrust.
• A hydrometer works on the principle of flotation.
• A ship floats because it displaces enough water to balance its weight.

Think. Analyse. Discover!

Physics is not just about memorising formulas. It is about understanding why things happen.

Observe carefully. Question logically. Explain scientifically.

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