Archimedes' Principle Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Archimedes' Principle.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

A fluid pushes up exactly as much as the displaced fluid would weigh.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Archimedes' Principle asks how mass, volume, pressure, and displacement determine the fluid interaction.

Common stuck point: Students often know a formula related to archimedes' principle but skip the recognition step: Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified?

Worked Examples

Example 1

medium
A wooden block of density 600 kg/m3600 \text{ kg/m}^3 floats in water. What fraction of its volume is below the surface?

Answer

VsubVblock=0.6\dfrac{V_{sub}}{V_{block}} = 0.6

First step

1
Floating condition: weight = buoyant force, so ρobjVg=ρfVsubg\rho_{obj} V g = \rho_f V_{sub} g.

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Example 2

medium
A 2 kg2 \text{ kg} metal object has volume 5×10−4 m35 \times 10^{-4} \text{ m}^3 and is fully submerged in water. Find its apparent weight. (ρ=1000\rho = 1000, g=10g = 10)

Example 3

medium
A boat of mass 400 kg400 \text{ kg} floats in fresh water. Find the volume of water displaced. (ρ=1000\rho=1000, g=10g=10)

Example 4

medium
A cubic block of side 0.1 m0.1 \text{ m} and density 1200 kg/m31200 \text{ kg/m}^3 is fully submerged in water (ρ=1000\rho=1000, g=10g=10). Find the net force and direction.

Example 5

hard
A 5 kg5 \text{ kg} object hangs from a spring scale. When lowered into water, the scale reads 32 N32 \text{ N}. Find the object's volume. (ρ=1000\rho = 1000, g=10g = 10)

Example 6

hard
A boat of mass 200 kg200 \text{ kg} and base area 5 m25 \text{ m}^2 floats in fresh water. By how much does it sink deeper when a 50 kg50 \text{ kg} passenger steps aboard? (ρ=1000\rho = 1000, g=10g = 10)

Example 7

hard
A boat of mass 1000 kg1000 \text{ kg} floats in a sealed pool of water sitting on a scale. A 30 kg30 \text{ kg} rock is dropped into the pool from the boat. What does the scale read (just the system) before vs. after? (g=10g=10)

Example 8

hard
A 0.5 kg0.5 \text{ kg} ball of volume 4×10−4 m34 \times 10^{-4} \text{ m}^3 is held submerged at rest. Released, what is its initial acceleration? (ρ=1000\rho=1000, g=10g=10)

Example 9

challenge
A crown allegedly of pure gold (ρAu=19300\rho_{Au}=19300) weighs 19.3 N19.3 \text{ N} in air and 18.1 N18.1 \text{ N} submerged in water (ρw=1000\rho_w=1000, g=10g=10). Is it pure gold?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
An object displaces 0.003 m30.003 \text{ m}^3 of water (ρ=1000\rho=1000, g=10g=10). By Archimedes' principle, find the buoyant force.

Example 2

easy
A submerged object displaces 2 kg2 \text{ kg} of water. Find the buoyant force (g=10g=10).

Example 3

easy
A ship floats by displacing water equal in weight to the ship's 50000 N50000 \text{ N}. What is the buoyant force?

Example 4

easy
An object weighs 40 N40 \text{ N} in air and 25 N25 \text{ N} in water. Find the weight of water displaced.

Example 5

easy
Find the volume of fluid displaced if the buoyant force is 50 N50 \text{ N} in water (ρ=1000\rho=1000, g=10g=10).

Example 6

easy
Only the submerged part of an object displaces fluid. If half is submerged, what fraction of full-submersion buoyancy acts?

Example 7

easy
A rock displaces 0.0008 m30.0008 \text{ m}^3 of water. Find the mass of water displaced (ρ=1000\rho=1000).

Example 8

easy
Two objects displace the same volume in the same fluid. Compare their buoyant forces.

Example 9

medium
A 0.6 kg0.6 \text{ kg} object of volume 0.0004 m30.0004 \text{ m}^3 is submerged in water (ρ=1000\rho=1000, g=10g=10). Find its apparent weight.

Example 10

medium
A crown of mass 1 kg1 \text{ kg} displaces 0.00006 m30.00006 \text{ m}^3 of water. Find its density and compare to gold (1930019300). (ρw=1000\rho_w=1000)

Example 11

medium
A block floats with 0.70.7 submerged in water (10001000). Find its density using Archimedes' principle.

Example 12

medium
A 5 N5 \text{ N} object is fully submerged and the buoyant force is 3 N3 \text{ N}. Find the net force and direction.

Example 13

medium
A boat of mass 800 kg800 \text{ kg} floats in water (ρ=1000\rho=1000, g=10g=10). Find the volume of water it displaces.

Example 14

medium
An object weighs 60 N60 \text{ N} in air, 50 N50 \text{ N} in water (10001000), and 52 N52 \text{ N} in oil. Find the oil's density. (g=10g=10)

Example 15

medium
A balloon displaces 3 m33 \text{ m}^3 of air (ρ=1.2\rho=1.2, g=10g=10). Find the buoyant (lift) force.

Example 16

medium
A 0.9extkg0.9 ext{ kg} object of volume 0.0001extm30.0001 ext{ m}^3 is submerged in water (ho=1000 ho=1000, g=10g=10). Find the buoyant force and apparent weight.

Example 17

medium
A floating object displaces 0.0024extm30.0024 ext{ m}^3 of water (ho=1000 ho=1000, g=10g=10). Find the object's weight.

Example 18

challenge
A 0.5 kg0.5 \text{ kg} object of volume 0.0003 m30.0003 \text{ m}^3 floats partly in water with a string pulling it down with tension 2 N2 \text{ N}. Find the submerged volume. (ρ=1000\rho=1000, g=10g=10)

Example 19

challenge
A hollow sphere of outer volume 0.002 m30.002 \text{ m}^3 and mass 1.5 kg1.5 \text{ kg} is placed in water (10001000, g=10g=10). Does it float, and if so what fraction is submerged?

Example 20

challenge
An ice cube (ρ=920\rho=920) floats in water (10001000). When it melts, does the water level rise, fall, or stay the same?

Example 21

easy
A fully submerged object displaces 0.002 m30.002 \text{ m}^3 of water. Find the buoyant force (ρ=1000\rho = 1000, g=10g = 10).

Example 22

easy
A submerged object displaces a fluid weighing 35 N35 \text{ N}. What is the buoyant force on it?

Example 23

easy
A swimmer fully submerges and displaces 60 L60 \text{ L} of water. Find the buoyant force. (ρ=1000\rho=1000, g=10g=10; 1 L=10−3 m31 \text{ L} = 10^{-3} \text{ m}^3)

Example 24

easy
A balloon of volume 0.5 m30.5 \text{ m}^3 is fully submerged in fresh water. Find the buoyant force. (ρ=1000\rho=1000, g=10g=10)

Example 25

easy
An object weighing 50 N50 \text{ N} in air weighs 30 N30 \text{ N} when submerged. Find the buoyant force.

Example 26

easy
What volume of water must be displaced for a buoyant force of 80 N80 \text{ N}? (ρ=1000\rho = 1000, g=10g = 10)

Example 27

medium
An iceberg has density 920 kg/m3920 \text{ kg/m}^3 and floats in seawater of density 1025 kg/m31025 \text{ kg/m}^3. What fraction is above the surface?

Example 28

medium
An object of volume 0.001 m30.001 \text{ m}^3 floats half-submerged in oil (ρoil=800\rho_{oil}=800). Find its mass. (g=10g=10)

Example 29

medium
A balloon filled with helium (ρHe=0.18 kg/m3\rho_{He}=0.18 \text{ kg/m}^3) has volume 2 m32 \text{ m}^3 in air (ρair=1.2\rho_{air}=1.2). Find the buoyant force on it (g=10g=10).

Example 30

medium
An object of mass 3 kg3 \text{ kg} has buoyant force 40 N40 \text{ N} when fully submerged in water. What is its volume? (ρ=1000\rho=1000, g=10g=10)

Example 31

medium
A floating block displaces 0.300.30 of its volume in water. Find its density. (ρf=1000\rho_f = 1000)

Example 32

hard
A block of density ρobj\rho_{obj} floats with fraction f=0.7f = 0.7 submerged in fluid A (ρA=1000\rho_A=1000). In fluid B it floats with fraction 0.50.5. Find ρB\rho_B.

Example 33

hard
A hot-air balloon and basket together have mass 400 kg400 \text{ kg}. The balloon's heated air has density 0.9 kg/m30.9 \text{ kg/m}^3; surrounding air is 1.21.2. Find the minimum balloon volume for liftoff. (g=10g=10)

Example 34

hard
A 2 kg2 \text{ kg} stone is tied to a 0.001 m30.001 \text{ m}^3 piece of wood (ρwood=600 kg/m3\rho_{wood} = 600 \text{ kg/m}^3). The system just barely floats in water (ρ=1000\rho=1000, g=10g=10). Find the stone's volume.

Example 35

hard
A submerged 1 kg1 \text{ kg} object of volume 2×10−4 m32 \times 10^{-4} \text{ m}^3 is held by a rope from above in water (ρ=1000\rho=1000, g=10g=10). Find the rope tension.

Example 36

challenge
An ice cube (ρice=920\rho_{ice}=920) floats in a glass of water (ρw=1000\rho_w=1000), with the cube fully fitting inside. The ice melts. Does the water level rise, fall, or stay the same?
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Related Concepts

Buoyancy

Background Knowledge

These ideas may be useful before you work through the harder examples.

buoyancy