Practice Density in Physics

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

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Quick Recap

Density is the amount of mass packed into a given volume. In physics, it helps explain why some materials float, sink, or create larger pressure.

Density tells you how tightly matter is packed. Heavy for its size means high density.

Showing a random 20 of 50 problems.

Example 1

medium

A gas in a sealed piston has density

1.2\text{ kg/m}^3

. The piston is pushed in so the volume drops from

4\text{ m}^3

1\text{ m}^3

(no gas added). Find the new density.

Example 2

medium

A river carries silt:

30 \text{ kg}

of sediment (

\rho=2600 \text{ kg/m}^3

) suspended in

1 \text{ m}^3

of water (

\rho=1000

). Find the mixture density.

Example 3

easy

Olive oil has density

920\text{ kg/m}^3

. Water is

1000\text{ kg/m}^3

. Will olive oil float on water?

Example 4

easy

Ice has density

920 \text{ kg/m}^3

and water

1000 \text{ kg/m}^3

. Will ice float on water?

Example 5

medium

1.5\text{ L}

bottle of cooking oil weighs

1.20\text{ kg}

. Find the oil's density in

\text{kg/m}^3

Example 6

medium

A wooden plank floats with

80\%

of its volume submerged. Water density is

1000 \text{ kg/m}^3

. Estimate the wood's density.

Example 7

challenge

A sphere of unknown radius and density

\rho = 2500\text{ kg/m}^3

has mass

1.05\text{ kg}

. Find its radius. (

V = \tfrac{4}{3}\pi r^3

Example 8

easy

True or false: a heavier object always has higher density than a lighter object.

Example 9

hard

A jeweler tests a

200\text{ g}

ring. In air it weighs

200\text{ g}

; submerged in water (which buoys it) it reads

182\text{ g}

on a balance. Find the ring's density. (

\rho_\text{water} = 1.00\text{ g/cm}^3

Example 10

easy

Convert a density of

2 \text{ g/cm}^3

\text{kg/m}^3

Example 11

medium

A graduated cylinder reads

40.0\text{ mL}

. A rock dropped in raises it to

58.0\text{ mL}

. The rock weighs

54\text{ g}

. Find its density in

\text{g/cm}^3

Example 12

medium

Two metals are mixed by volume:

0.0010\text{ m}^3

of metal A (

\rho=8000

) and

0.0010\text{ m}^3

of metal B (

\rho=4000

). Find the average density.

Example 13

hard

An alloy is

40\%

copper by mass (

\rho=8960

) and

60\%

zinc by mass (

\rho=7140

). Find the alloy's density. (Use

1/\rho_\text{alloy} = w_\text{Cu}/\rho_\text{Cu} + w_\text{Zn}/\rho_\text{Zn}

Example 14

challenge

A block of density

\rho_b

floats at the boundary between oil (

\rho_o=750

) on top and water (

\rho_w=1000

) below, with

30\%

of its volume in oil and

70\%

in water. Find

\rho_b

Example 15

medium

500 \text{ g}

crown has volume

50 \text{ cm}^3

. Pure gold is

19.3 \text{ g/cm}^3

. Is the crown pure gold?

Example 16

hard

Equal masses of liquid A (

\rho=600

) and liquid B (

\rho=1200

) — say,

6\text{ kg}

each — are mixed in a container where they stay separated. Find the average density of the combined column.

Example 17

easy

A metal cube has density

8000 \text{ kg/m}^3

and mass

16 \text{ kg}

. Find its volume.

Example 18

easy

Aluminum has density

2700\text{ kg/m}^3

. What is the mass of

0.05\text{ m}^3

of aluminum?

Example 19

medium

A submarine has total volume

50\text{ m}^3

and mass

48000\text{ kg}

with empty ballast. Water is

1000\text{ kg/m}^3

. Will it float, sink, or be neutrally buoyant?

Example 20

medium

An ice cube of density

920\text{ kg/m}^3

floats in seawater of density

1025\text{ kg/m}^3

. What fraction of the cube is submerged?

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Related Concepts

Mass Pressure Buoyancy