Buoyancy Examples: 47 Problems with Answers

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

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

Concept Recap

Buoyancy is the upward force a fluid exerts on an object that is partly or fully immersed in it.

Water pushes up more on the bottom of an object than on the top, so the object feels an upward lift.

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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: Buoyancy asks how mass, volume, pressure, and displacement determine the fluid interaction.

Common stuck point: Students often know a formula related to buoyancy 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

3 \text{ kg}

rock of volume

0.001 \text{ m}^3

is lowered into water (

\rho=1000

g=10

) by a rope. Find the tension in the rope when the rock is fully submerged and at rest.

Answer

T = 20 N

First step

Weight:

W = mg = 3 \times 10 = 30 \text{ N}

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Example 2

medium

A boat displaces

1.5 \text{ m}^3

of fresh water when floating (

\rho=1000

g=10

). Find the total weight of the boat and cargo.

Example 3

hard

A balloon weighs

30 \text{ N}

(envelope + gas) and has volume

4 \text{ m}^3

in air (

\rho=1.2

g=10

). What payload (extra weight) can it lift while remaining floating?

Example 4

hard

A cylinder of cross-section

0.0002 \text{ m}^2

and height

0.4 \text{ m}

has density

500 \text{ kg/m}^3

. It floats vertically in water (

\rho=1000

g=10

). Find the length of cylinder submerged.

Example 5

challenge

A balloon of volume

V

filled with helium (

\rho_{He}=0.18

) sits in air (

\rho_{\text{air}}=1.2

g=10

). The envelope weighs

5 \text{ N}

. Find the minimum

V

so the balloon just lifts off (zero payload).

Practice Problems

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

Example 1

easy

An object displaces

0.002 \text{ m}^3

of water (

\rho=1000

g=10

). Find the buoyant force.

Example 2

easy

A fully submerged ball displaces

0.001 \text{ m}^3

in water. Find the buoyant force. (

\rho=1000

g=10

)

Example 3

easy

The buoyant force on a floating log equals its weight of

300 \text{ N}

. What is the buoyant force?

Example 4

easy

An object weighs

50 \text{ N}

in air and

30 \text{ N}

when submerged. Find the buoyant force.

Example 5

easy

Will buoyancy be larger in water (

1000

) or oil (

800

) for the same submerged volume?

Example 6

easy

A submerged object has buoyant force

40 \text{ N}

in water (

\rho=1000

g=10

). Find its volume.

Example 7

easy

A boat floats. Compared to its weight, the buoyant force is: greater, less, or equal?

Example 8

easy

An object of volume

0.003 \text{ m}^3

is half submerged in water (

\rho=1000

g=10

). Find the buoyant force.

Example 9

medium

2 \text{ kg}

block of volume

0.0015 \text{ m}^3

is fully submerged in water (

\rho=1000

g=10

). Find the net force and whether it sinks.

Example 10

medium

An object floats with

60\%

submerged in water (

\rho=1000

). Find its density.

Example 11

medium

0.2 \text{ kg}

object of volume

0.0005 \text{ m}^3

is held fully under water by a string. Find the string tension. (

\rho=1000

g=10

)

Example 12

medium

An iceberg (

\rho=920

) floats in seawater (

\rho=1025

). What fraction is below the surface?

Example 13

medium

A balloon of volume

5 \text{ m}^3

in air (

\rho=1.2

g=10

) has total mass

4 \text{ kg}

. Find the net upward force.

Example 14

medium

A crown weighs

20 \text{ N}

in air and

18 \text{ N}

in water. Find its volume. (

\rho=1000

g=10

)

Example 15

medium

A wooden cube (

\rho=600

) of side

0.1 \text{ m}

floats in water (

1000

). Find the depth it sinks below the surface.

Example 16

medium

Two identical blocks float, one in water (

1000

) and one in alcohol (

790

). Which floats higher (smaller submerged fraction)?

Example 17

medium

A steel ball (

\rho=7800

) of volume

0.0002 \text{ m}^3

is fully submerged in water (

1000

g=10

). Find its apparent weight.

Example 18

challenge

A block of density

900 \text{ kg/m}^3

sits at the interface of oil (

\rho=800

) on top and water (

\rho=1000

) below, with part in each. What fraction of its volume is in the water?

Example 19

challenge

1 \text{ kg}

object of volume

0.0005 \text{ m}^3

rests on the bottom of a tank. Find the normal force from the floor when submerged in water. (

\rho=1000

g=10

)

Example 20

challenge

A hydrometer of mass

0.02 \text{ kg}

and uniform cross-section

0.0001 \text{ m}^2

floats in a liquid. It sinks to a depth of

0.25 \text{ m}

. Find the liquid's density. (

g=10

)

Example 21

easy

A diver pushes a fully submerged ball that displaces

0.005 \text{ m}^3

of water (

\rho=1000

g=10

). Find the buoyant force.

Example 22

easy

A cube displaces

0.0008 \text{ m}^3

of seawater (

\rho=1025

g=10

). Find the buoyant force.

Example 23

easy

A buoyant force of

25 \text{ N}

acts on a fully submerged object in water (

\rho=1000

g=10

). What volume does it occupy?

Example 24

easy

A block of volume

0.004 \text{ m}^3

is one-quarter submerged in water (

\rho=1000

g=10

). Find the buoyant force.

Example 25

easy

A helium balloon of volume

0.5 \text{ m}^3

sits in air (

\rho=1.2

g=10

). Find the buoyant force air exerts on it.

Example 26

medium

A block of density

750 \text{ kg/m}^3

floats in water (

\rho=1000

). What fraction of its volume is below the surface?

Example 27

medium

A raft of volume

0.6 \text{ m}^3

and mass

200 \text{ kg}

floats in fresh water (

\rho=1000

g=10

). What additional mass can it carry before it submerges?

Example 28

medium

A solid sphere with apparent weight

14 \text{ N}

in water has actual weight

20 \text{ N}

in air. Find its volume. (

\rho=1000

g=10

)

Example 29

medium

An ice cube (

\rho=917

) floats in fresh water (

\rho=1000

). What fraction of the cube is above the surface?

Example 30

medium

A balloon of volume

2 \text{ m}^3

has total mass (envelope + gas)

1.5 \text{ kg}

in air (

\rho=1.2

g=10

). Find its acceleration when released. Ignore drag.

Example 31

medium

A swimmer of mass

60 \text{ kg}

floats with

95\%

of her body submerged in fresh water (

\rho=1000

g=10

). Find her body's average density.

Example 32

medium

0.5 \text{ kg}

block of volume

0.0006 \text{ m}^3

floats with part of it submerged in water (

\rho=1000

g=10

). Find the submerged volume.

Example 33

medium

A balloon of volume

4 \text{ m}^3

has buoyant force

48 \text{ N}

in air. Find the air density. (

g=10

)

Example 34

hard

A wooden block of density

600 \text{ kg/m}^3

floats in water (

\rho=1000

). A child presses it down until it is fully submerged. The block has volume

0.002 \text{ m}^3

(

g=10

). Find the downward force the child must apply.

Example 35

hard

0.3 \text{ kg}

ball of volume

0.0004 \text{ m}^3

is released from rest underwater (

\rho=1000

g=10

). Find its initial acceleration (ignore drag).

Example 36

hard

A submarine of constant volume

200 \text{ m}^3

has mass

190{,}000 \text{ kg}

when fully ballasted. In seawater (

\rho=1025

g=10

), is it sinking, rising, or neutrally buoyant?

Example 37

hard

An object weighs

25 \text{ N}

in air,

20 \text{ N}

in water (

\rho=1000

), and

19 \text{ N}

in another liquid. Find that liquid's density. (

g=10

)

Example 38

hard

A ship floats in fresh water (

\rho=1000

). When it sails into seawater (

\rho=1025

), does it ride higher or lower in the water?

Example 39

hard

A hollow steel cube has external volume

0.001 \text{ m}^3

and mass

0.8 \text{ kg}

. Will it float in water (

\rho=1000

g=10

Example 40

hard

5 \text{ kg}

rock of volume

0.002 \text{ m}^3

sits on the bottom of a tank of water (

\rho=1000

g=10

). Find the normal force from the tank floor.

Example 41

hard

A block of density

400 \text{ kg/m}^3

and volume

0.001 \text{ m}^3

is held under water by a string from below (

\rho=1000

g=10

). Find the tension in the string.

Example 42

challenge

A cube of side

0.1 \text{ m}

floats at the interface of oil (

\rho=800

) on top and water (

\rho=1000

) below. Half its volume is in each. Find the cube's density. (

g=10

)

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Related Concepts

Pressure Density Weight Archimedes' Principle

Background Knowledge

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

pressuremass densityweight