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 kg/m31.2\text{ kg/m}^3. The piston is pushed in so the volume drops from 4 m34\text{ m}^3 to 1 m31\text{ m}^3 (no gas added). Find the new density.

Example 2

medium
A river carries silt: 30 kg30 \text{ kg} of sediment (ρ=2600 kg/m3\rho=2600 \text{ kg/m}^3) suspended in 1 m31 \text{ m}^3 of water (ρ=1000\rho=1000). Find the mixture density.

Example 3

easy
Olive oil has density 920 kg/m3920\text{ kg/m}^3. Water is 1000 kg/m31000\text{ kg/m}^3. Will olive oil float on water?

Example 4

easy
Ice has density 920 kg/m3920 \text{ kg/m}^3 and water 1000 kg/m31000 \text{ kg/m}^3. Will ice float on water?

Example 5

medium
A 1.5 L1.5\text{ L} bottle of cooking oil weighs 1.20 kg1.20\text{ kg}. Find the oil's density in kg/m3\text{kg/m}^3.

Example 6

medium
A wooden plank floats with 80%80\% of its volume submerged. Water density is 1000 kg/m31000 \text{ kg/m}^3. Estimate the wood's density.

Example 7

challenge
A sphere of unknown radius and density ρ=2500 kg/m3\rho = 2500\text{ kg/m}^3 has mass 1.05 kg1.05\text{ kg}. Find its radius. (V=43πr3V = \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 g200\text{ g} ring. In air it weighs 200 g200\text{ g}; submerged in water (which buoys it) it reads 182 g182\text{ g} on a balance. Find the ring's density. (ρwater=1.00 g/cm3\rho_\text{water} = 1.00\text{ g/cm}^3.)

Example 10

easy
Convert a density of 2 g/cm32 \text{ g/cm}^3 to kg/m3\text{kg/m}^3.

Example 11

medium
A graduated cylinder reads 40.0 mL40.0\text{ mL}. A rock dropped in raises it to 58.0 mL58.0\text{ mL}. The rock weighs 54 g54\text{ g}. Find its density in g/cm3\text{g/cm}^3.

Example 12

medium
Two metals are mixed by volume: 0.0010 m30.0010\text{ m}^3 of metal A (ρ=8000\rho=8000) and 0.0010 m30.0010\text{ m}^3 of metal B (ρ=4000\rho=4000). Find the average density.

Example 13

hard
An alloy is 40%40\% copper by mass (ρ=8960\rho=8960) and 60%60\% zinc by mass (ρ=7140\rho=7140). Find the alloy's density. (Use 1/ρalloy=wCu/ρCu+wZn/ρZn1/\rho_\text{alloy} = w_\text{Cu}/\rho_\text{Cu} + w_\text{Zn}/\rho_\text{Zn}.)

Example 14

challenge
A block of density ρb\rho_b floats at the boundary between oil (ρo=750\rho_o=750) on top and water (ρw=1000\rho_w=1000) below, with 30%30\% of its volume in oil and 70%70\% in water. Find ρb\rho_b.

Example 15

medium
A 500 g500 \text{ g} crown has volume 50 cm350 \text{ cm}^3. Pure gold is 19.3 g/cm319.3 \text{ g/cm}^3. Is the crown pure gold?

Example 16

hard
Equal masses of liquid A (ρ=600\rho=600) and liquid B (ρ=1200\rho=1200) — say, 6 kg6\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 kg/m38000 \text{ kg/m}^3 and mass 16 kg16 \text{ kg}. Find its volume.

Example 18

easy
Aluminum has density 2700 kg/m32700\text{ kg/m}^3. What is the mass of 0.05 m30.05\text{ m}^3 of aluminum?

Example 19

medium
A submarine has total volume 50 m350\text{ m}^3 and mass 48000 kg48000\text{ kg} with empty ballast. Water is 1000 kg/m31000\text{ kg/m}^3. Will it float, sink, or be neutrally buoyant?

Example 20

medium
An ice cube of density 920 kg/m3920\text{ kg/m}^3 floats in seawater of density 1025 kg/m31025\text{ kg/m}^3. What fraction of the cube is submerged?
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Related Concepts

MassPressureBuoyancy