Topic 6.116 min read
Upthrust and Archimedes' Principle
Upthrust is the net upward force exerted by a fluid on an immersed body. Archimedes' principle states that this force equals the weight of the displaced fluid: Fb = ρf gV_d.
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Beginner Level
An object placed in water feels lighter because the water pushes upward on it. This upward force is called upthrust or buoyant force. It occurs because pressure is greater at the deeper bottom surface than at the upper surface.
- F_b
- upthrust (N)
- ρ_f
- fluid density (kg m⁻³)
- V_d
- displaced-fluid volume (m³)
When to use: Use for a body wholly or partly immersed in a fluid.
Scientists connected to this topic
Known for: Upthrust equals the weight of fluid displaced (Archimedes’ principle).
Wikimedia Commons — Domenico Fetti, 17th century. Later painting, not a lifetime portrait.
Recommended for Class 11
6.1 Upthrust and Archimedes' Principle
Overview
Liquids and gases are fluids. Any object immersed in a fluid experiences an upward buoyant force because fluid pressure increases with depth. This principle explains why some bodies rise, some remain suspended and others sink.
Learning Outcomes
- Define upthrust and buoyant force.
- Explain upthrust using pressure difference.
- State and derive Archimedes' principle.
- Calculate buoyant force and displaced volume.
- Relate upthrust to apparent loss of weight.
- Predict whether an object rises, sinks or remains suspended.
Upthrust
Upthrust, also called buoyant force, is the net upward force exerted by a fluid on a body that is partly or completely immersed in it. The force acts whether the body floats, sinks or remains suspended.
Pressure in a fluid increases with depth. The lower surface of an immersed body therefore experiences a larger upward pressure force than the downward pressure force on its upper surface. Their difference is the upthrust.
| Comparison | Motion |
|---|---|
| F_b > W | Net force upward; body rises |
| Fb = W | Body floats or remains suspended in equilibrium |
| F_b < W | Net force downward; body sinks |
Archimedes' Principle
- F_b
- buoyant force or upthrust (N)
- ρ_f
- density of fluid (kg m⁻³)
- g
- gravitational field strength (m s⁻²)
- V_d
- volume of displaced fluid (m³)
When to use: Use the volume of the immersed part, not automatically the total object volume.
Intermediate Level
Derivation for an Immersed Cylinder
Consider a vertical cylinder of cross-sectional area A and height h immersed in a liquid of density ρ. Its top and bottom are at depths h₁ and h₂, so h₂ - h₁ = h.
Pressure force equals pressure multiplied by area:
The horizontal pressure forces cancel. The net vertical upthrust is the lower force minus the upper force:
Since Ah is the cylinder volume and equals the displaced-liquid volume V_d:
Apparent Weight
Upthrust reduces the supporting force needed to hold an immersed object, so it appears lighter in the fluid.
When to use: Use when apparent loss of weight is given.
Units and Dimensions
Upthrust is a force, so its SI unit is newton and its dimensions are [MLT⁻²].
Solved Numerical Examples
Textbook Example 6.1: Cubic Wooden Block
A cubic block is completely immersed in water. Each side is 10 cm. Find the upthrust.
- L = 10 cm = 0.10 m
- ρwater = 1000 kg m⁻³
- g = 9.8 m s⁻²
Vd = L³
Vd = (0.10 m)³
Vd = 0.001 m³
Fb = ρgVd
Fb = (1000)(9.8)(0.001)
Final answer: Fb = 9.8 N
Example 2: Partly Immersed Body
A floating body displaces 0.025 m³ of water. Find its upthrust.
- Vd = 0.025 m³
- ρwater = 1000 kg m⁻³
- g = 9.8 m s⁻²
Fb = ρgVd
Fb = (1000)(9.8)(0.025)
Final answer: Fb = 245 N
Textbook Assignment 6.1: Iron Object
An iron object of density 7.8 g cm⁻³ appears 200 N lighter in water. Find its volume and weight in air.
- Fb = 200 N
- ρwater = 1000 kg m⁻³
- ρiron = 7.8 g cm⁻³ = 7800 kg m⁻³
- g = 9.8 m s⁻²
Fb = ρwater gV
V = Ffracbρwater g
V = 200/((1000)(9.8))
V = 0.0204 m³
m = ρiron V
m = (7800)(0.0204) = 159.2 kg
Wair = mg
Wair = (159.2)(9.8)
Final answer: V ≈ 2.04 × 10⁻² m³ and Wair ≈ 1.56 × 10³ N
Real-Life Applications
- Ships float by displacing water whose weight equals the ship's weight.
- Submarines change ballast-tank contents to rise or sink.
- Hydrometers compare liquid density by their immersed depth.
- Life jackets increase displaced volume and upthrust.
- Hot-air and helium balloons experience buoyancy in air.
Common Mistakes
- Using object density instead of fluid density in Fb = ρf gV_d.
- Using total object volume when only part is immersed.
- Forgetting to convert cm³ to m³.
- Assuming upthrust acts only on floating bodies.
- Saying upthrust always equals object weight.
- Adding upthrust to weight when finding apparent weight.
Short-Question Preparation
Q. Define upthrust.
A. Upthrust is the net upward force exerted by a fluid on a partly or completely immersed body.
Q. State Archimedes' principle.
A. An immersed body experiences upthrust equal to the weight of the fluid it displaces.
Q. Why does upthrust act?
A. Fluid pressure increases with depth, so the upward pressure force on the lower surface is greater than the downward force on the upper surface.
Q. What is apparent loss of weight?
A. It is Wair - Wapparent and equals the upthrust.
Long-Question Preparation
Q. State and derive Archimedes' principle for a cylinder.
A. 1. Consider a cylinder of area A and height h in fluid density ρ. 2. Its top and bottom depths are h₁ and h₂. 3. P₁ = ρgh₁ and P₂ = ρgh₂. 4. F₁ = P₁A and F₂ = P₂A. 5. Upthrust Fb = F₂ - F₁. 6. Fb = ρgA(h₂ - h₁). 7. Since h₂ - h₁ = h, Fb = ρgAh. 8. Since Ah = Vd, Fb = ρgVd. 9. Because ρVd is displaced-fluid mass, Fb equals its weight.
Sticky Notes
- Pressure increases with depth.
- Upthrust = lower force - upper force.
- Fb = ρf gVd.
- Use immersed volume.
- Apparent loss of weight = F_b.
- Fb > W rises; Fb = W equilibrium; Fb < W sinks.
60-Second Revision
Summary
A pressure difference across an immersed body produces upthrust. Derivation for a cylinder gives Fb = ρf gV_d, proving that buoyant force equals the weight of displaced fluid. Comparing upthrust with weight predicts rising, equilibrium or sinking.
Ask-the-Tutor Modes
- Explain upthrust simply.
- Show the derivation one line at a time.
- Help choose displaced volume.
- Explain apparent weight.
- Check my unit conversions.
- Test me with an MCQ.
Scientists connected to this topic
Known for: Upthrust equals the weight of fluid displaced (Archimedes’ principle).
Wikimedia Commons — Domenico Fetti, 17th century. Later painting, not a lifetime portrait.
Exam Focus
Exam Focus
Important points
- Definition
- Statement
- Pressure derivation
- Apparent weight
- Float-rise-sink conditions
Important formulas
- Fb = ρf gVd
- Wapparent = Wair - Fb
- P = ρgh
Common exam traps
- Wrong density
- Wrong volume
- Unit conversion
- Assuming buoyancy only when floating
Short question tips
- Name pressure difference as the cause.
Long question structure
Diagram → pressures → forces → difference → V = Ah → principle statement.
Common Mistakes
Common Mistakes
- Mistake
Use fluid density.
- Mistake
Use displaced volume.
- Mistake
Convert volume units.
- Mistake
Upthrust acts on sinking objects too.
- Mistake
Apparent weight = actual weight - upthrust.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Pressure difference causes it.
Fb = ρf gVd.
Use immersed volume.
Apparent loss = Fb.
Upthrust equals the weight of displaced fluid.
Fb = ρf gVd
- Definition
- Upthrust equals the weight of displaced fluid.
- Formula
- Fb = ρf gVd
- Example
- A 0.001 m³ cube in water has Fb = 9.8 N.
- Critical warning
- Do not use the object's density in the buoyancy formula.
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Exam Practice
Important Short Question
Q1. Define upthrust.
Important Short Question
Q2. State Archimedes' principle.
Conceptual Question
Q3. Why does an immersed object appear lighter?
Long Question Preparation
Q4. Derive Archimedes' principle.