Practice Archimedes' Principle in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

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 2

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 3

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

Example 4

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 5

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 6

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 7

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

Example 8

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

Example 9

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 10

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 11

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 12

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 13

medium
A boat displaces more water when more cargo is loaded. Why must this happen for it to keep floating?

Example 14

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

Example 15

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 16

medium
A steel ball sinks but a steel ship floats. Why?

Example 17

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

Example 18

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 19

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 20

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)
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Related Concepts

Buoyancy