Mass, Weight & Density

Learn it by playing

Answer these questions to earn energy, then fish and explore. No account needed.

For teachers: ready-to-use lesson slides, revision notes, diagrams for Mass, Weight & Density (Physics, CIE) — use them in your lesson, or run the topic as a live class game.

Notes

Mass & Weight

**Mass** is a measure of the quantity of matter in an object; it is a **scalar** quantity measured in **kg** (or g).
**Weight** is the gravitational force on an object with mass; it is a **vector** quantity measured in **N**.
Mass is constant everywhere; weight depends on gravitational field strength.
Equation: **W = m × g**, where g = gravitational field strength (N/kg).
On Earth, g ≈ 9.8 N/kg; on the Moon, g ≈ 1.6 N/kg.
A **balance** measures mass (kg); a **force meter** (newton meter) measures weight (N).

Density

**Density** is the mass per unit volume of a material: **ρ = m / V**.
Units: kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³).
Low-density materials have low mass for a given volume; high-density materials have high mass.
Gases are less dense than solids/liquids because particles are more spread out.
Volume of regular shapes: cube (side³), sphere (4/3πr³), cylinder (πr²h).

Measuring Density of Regular Solids

Use a **digital balance** to measure mass.
Measure dimensions with a ruler, Vernier calipers, or micrometer.
Calculate volume from dimensions, then density = mass / volume.
Repeat measurements and take averages to reduce random errors.

Measuring Density of Irregular Solids

Use a **eureka can** (displacement can) and measuring cylinder.
Fill can to just below spout; place empty cylinder under spout.
Lower object gently; collect displaced water; volume = volume of object.
Alternatively, submerge object in measuring cylinder with water; rise in level = volume.
Density = mass / displaced volume.

Measuring Density of Liquids

Place empty measuring cylinder on digital balance; record mass.
Add known volume of liquid; record new mass.
Mass of liquid = (mass of cylinder + liquid) – (mass of empty cylinder).
Density = mass of liquid / volume.

Floating & Sinking

An object floats if its density is **less** than the fluid's density; sinks if **greater**.
**Upthrust** is an upward force on a submerged object, opposite to weight.
Object floats when upthrust = weight; sinks when upthrust < weight.
Upthrust depends on fluid density and volume of fluid displaced.
Example: polystyrene (0.05 g/cm³) floats on water (1.0 g/cm³); iron (7.9 g/cm³) sinks.

Floating Liquids (Extended)

A less dense liquid floats on a denser liquid if they do not mix.
For an object to sink in a liquid, object density must be greater than liquid density.
Example: potassium (0.862 g/cm³) sinks in liquid paraffin (0.825 g/cm³) but floats in denser oils.

Particle arrangement in solids, liquids, and gases. Solids have closely packed particles in fixed positions; liquids have close but randomly arranged particles; gases have widely spaced particles moving freely.

Practice questions

Free preview — 8 of 40 questions. Sign up to see them all.

1.Which of the following quantities is weight an example of?
Easy
- AForce
- BMass
- CAcceleration
- DField strength
2.Which of the following statements about mass or weight is true?
Easy
- AWeight is measured in Newtons
- BWeight is measured in kilograms
- CMass = weight × gravitational field strength
- DMass is a force
3.How is the weight of an object defined?
Easy
- AThe gravitational force acting on an object with mass
- BThe force of the ground pushing on an object
- CA measure of the quantity of matter of an object at rest to the observer
- DThe mass per unit volume of an object
4.Which row in the table gives the correct units for mass and for weight? A: Mass kg, Weight kg B: Mass N, Weight kg C: Mass N, Weight N D: Mass kg, Weight N
Easy
- AD
- BA
- CB
- DC
5.Which of the following quantities is measured in kilograms?
Easy
- Amass
- Bweight
- Cpressure
- Ddensity
6.Which statement about the mass and the weight of an object is correct?
Easy
- AThey have different units.
- BThey are both affected by changes in the acceleration of free fall.
- CThey are both forces.
- DWeight is calculated by dividing mass by the acceleration of free fall.
7.The gravitational field strength on the Moon is 1.6 N/kg. An astronaut has a mass of 75 kg. What is the weight of the astronaut on the Moon?
Easy
- A120 N
- B47 N
- C75 N
- D740 N
8.Which unit is a unit of weight?
Easy
- Akilonewton
- Bkilogram
- Ckilojoule
- Dkilometre

More questions

9.A shopkeeper pours rice into a dish that hangs from a spring balance. He records the reading. A customer buys some pasta. The shopkeeper notices that the reading on the spring balance, with just pasta in the dish, is the same as it was with just rice in the dish. Which quantity must be the same for the rice and for the pasta?
Medium
- Aweight
- Bdensity
- Ctemperature
- Dvolume
10.A student determines the density of an irregularly shaped stone. The stone is slowly lowered into a measuring cylinder partly filled with water. Which other apparatus does the student need to calculate the density of the irregularly shaped stone?
Medium
- Aa balance
- Ba thermometer
- Ca metre rule
- Da stop-watch
11.An object has a mass of 4.0 kg on Earth, where the acceleration of free fall is 9.8 m/s². The object is taken to the Moon, where the acceleration of free fall is 1.6 m/s². Which row gives the correct mass and weight of the object on the Moon? A: mass 2.5 kg, weight 4.0 N B: mass 4.0 kg, weight 6.4 N C: mass 4.0 kg, weight 39 N D: mass 6.4 kg, weight 39 N
Medium
- AB
- BA
- CC
- DD
12.Which piece of equipment is used to measure the mass of an object?
Medium
- AA balance
- BA burette
- CA thermometer
- DA trundle wheel
13.A baker uses a balance to weigh out some ingredients to make bread. She weighs out some white flour, then she weighs out some wholemeal flour. She notices that the reading on the balance is the same for both types of flour. The baker can conclude that the two flours have the same:
Medium
- Aweight
- Bvolume
- Cdensity
- Dinternal energy
14.The diagram shows a measuring cylinder containing a liquid, and that same measuring cylinder when it empty. The empty cylinder has a mass of 30 g. The cylinder with liquid has a mass of 93 g and the liquid volume is 20 cm³. What is the density of the liquid?
Medium
- A3.00 g/cm³
- B6.30 g/cm³
- C0.33 g/cm³
- D0.16 g/cm³
15.A geologist wants to determine the density of an object shown below. What needs to be known in order to calculate its density?
Medium
- AThe volume of the cone and the mass of the cone.
- BThe radius of the base of the cone and the weight of the cone.
- CThe surface area of the base of the cone and the height of the cone.
- DThe height of the cone and the mass of the cone.
16.Two beams have the same rectangular cross section, but one is longer than the other. Both beams are made from the same material. Which quantity is the same in both beams?
Medium
- AThe density
- BThe volume
- CThe weight
- DThe mass
17.A student wants to measure the density of a piece of rock. She starts by measuring its mass, and finds that it is 2500 g. Next she puts 500 cm³ of water into a large measuring cylinder, then adds the rock. The level in the measuring cylinder rises to 800 cm³. What is the density of the rock?
Medium
- A8.33 g/cm³
- B3.125 g/cm³
- C0.12 g/cm³
- D0.32 g/cm³
18.Some unknown liquid in a beaker has a mass of 200 g and a volume of 230 cm³. The density of water is 1.0 g/cm³. How does the density of the unknown liquid compare with the density of water?
Medium
- AIts density is less than the density of water
- BIts density is greater than the density of water
- CIts density is the same as the density of water
- DWith the information given, it is impossible to tell.
19.The two diagrams below show a measuring cylinder. In the diagram on the left, the measuring cylinder is empty. In the diagram on the right, the measuring cylinder contains a liquid. The empty cylinder has a mass of 40 g. The cylinder with liquid has a mass of 110 g and the liquid volume is 25 cm³. What is the density of the liquid?
Medium
- A2.80 g/cm³
- B5.00 g/cm³
- C0.28 g/cm³
- D3.57 g/cm³
20.A lump of butter has a volume of 350 cm³ and a mass of 319 g. What is the density of the butter?
Medium
- A0.911 g/cm³
- B1.10 g/cm³
- C1.00 g/cm³
- D31 g/cm³
21.A cube of side length 5 cm is placed on a mass balance. The balance reads 128 g. What is the density of the cube?
Medium
- A1.024 g/cm³
- B0.20 g/cm³
- C5.12 g/cm³
- D4.88 g/cm³
22.An astronaut has a mass of 80 kg on the Earth. The gravitational field strength on the Moon is 1.6 N/kg. What is the weight of the astronaut on the Moon?
Medium
- A128 N
- B50 kg
- C800 N
- D80 kg
23.The density of a block of wood is 2.7 g/cm³ and a mass of 583.8 g. What is its volume?
Medium
- A216.2 cm³
- B0.5 cm³
- C21.6 cm³
- D1574.9 cm³
24.Two objects P and Q are placed in a beaker containing a liquid. Object P floats in the liquid and object Q sinks. Which row for the densities of object P, object Q and the liquid is possible? A: P=1.2, Q=0.6, liquid=0.8 B: P=1.2, Q=1.4, liquid=1.0 C: P=11.3, Q=8.9, liquid=13.6 D: P=11.3, Q=19.3, liquid=13.6
Hard
- AD
- BA
- CB
- DC
25.A measuring cylinder contains 30 cm³ of a liquid. Some more of the liquid is added until the liquid level reaches the 50 cm³ mark. The reading on the balance increases by 30 g. What is the density of the liquid?
Hard
- A1.5 g/cm³
- B0.60 g/cm³
- C0.67 g/cm³
- D1.7 g/cm³
26.A space rocket travels to the Moon. The acceleration of free fall is greater on the Earth than it is on the Moon. How do the mass and weight of the space rocket on the Moon compare with their values on the Earth?
Hard
- Amass same as on Earth, weight less than on Earth
- Bmass less, weight same
- Cmass less, weight more
- Dmass same, weight more
27.The table shows the mass and the volume of two objects, P and Q. The objects are placed in a tank of water which has a density of 1.0 g/cm³. Object P: mass 15 g, volume 5 cm³. Object Q: mass 15 g, volume 20 cm³. Which statement is correct?
Hard
- AObject Q floats because its density is less than the density of water.
- BObject P floats because its density is greater than the density of water.
- CObject P sinks because its mass is equal to the mass of object Q.
- DObject Q sinks because its volume is greater than the volume of object P.
28.A teacher has two blocks of the same material. Block A has a mass of 200 g and a volume of 100 cm³. Block B has a mass of 400 g. What is the volume of block B?
Hard
- A200 cm³
- B50 cm³
- C100 cm³
- D400 cm³
29.A student measures the mass of a liquid as 250 g and its volume as 200 cm³. She then pours out half the liquid. What is the density of the remaining liquid?
Hard
- A1.25 g/cm³
- B2.5 g/cm³
- C0.625 g/cm³
- D0.8 g/cm³
30.An object has a weight of 50 N on Earth where g = 10 N/kg. What is its mass?
Hard
- A5 kg
- B0.2 kg
- C50 kg
- D500 kg
31.A piece of metal has a density of 8.9 g/cm³ and a volume of 10 cm³. It is cut into two equal halves. What is the density of one half?
Hard
- A8.9 g/cm³
- B4.45 g/cm³
- C17.8 g/cm³
- D0.89 g/cm³
32.A liquid has a density of 0.8 g/cm³. A solid object has a mass of 120 g and a volume of 100 cm³. When placed in the liquid, the object will:
Hard
- Asink
- Bfloat
- Cremain suspended at any depth
- Dpartially float with half submerged
33.A force meter (newton meter) is used to measure the weight of an object on Earth. The reading is 20 N. The object is then taken to a planet where gravitational field strength is half that of Earth. What will be the reading on the force meter?
Hard
- A10 N
- B20 N
- C40 N
- D5 N
34.A student uses a measuring cylinder to measure the volume of a stone by water displacement. The initial water level is 40 cm³. After adding the stone, the level is 55 cm³. The stone's mass is 45 g. What is its density?
Hard
- A3.0 g/cm³
- B0.33 g/cm³
- C1.22 g/cm³
- D0.82 g/cm³
35.A bottle contains 500 cm³ of cooking oil of density 0.9 g/cm³. What is the mass of the oil?
Hard
- A450 g
- B555.6 g
- C500 g
- D0.0018 g
36.Which of the following correctly describes the relationship between mass and weight?
Hard
- AWeight is mass multiplied by gravitational field strength.
- BMass is weight multiplied by gravitational field strength.
- CWeight is mass divided by gravitational field strength.
- DMass and weight are the same quantity.
37.A student wants to measure the density of a liquid. She places an empty measuring cylinder on a balance and records the mass as 50 g. She then pours 100 cm³ of the liquid into the cylinder and records the new mass as 130 g. What is the density of the liquid?
Hard
- A0.8 g/cm³
- B1.3 g/cm³
- C0.5 g/cm³
- D1.0 g/cm³
38.A block of wood floats in water with half its volume submerged. The density of water is 1.0 g/cm³. What is the density of the wood?
Hard
- A0.5 g/cm³
- B1.0 g/cm³
- C2.0 g/cm³
- D0.25 g/cm³
39.A student wants to determine the density of a liquid. She places an empty measuring cylinder on a digital balance and records the mass as 50 g. She then pours 100 cm³ of the liquid into the cylinder and records the new mass as 130 g. What is the density of the liquid?
Hard
- A0.80 g/cm³
- B1.30 g/cm³
- C0.50 g/cm³
- D1.80 g/cm³
40.A student uses a measuring cylinder to measure the volume of a stone by water displacement. The initial water level is 40 cm³. After adding the stone, the level rises to 65 cm³. The mass of the stone is 75 g. What is the density of the stone?
Hard
- A3.0 g/cm³
- B1.875 g/cm³
- C0.533 g/cm³
- D2.0 g/cm³

Slides

Mass & Weight

Mass is a measure of the quantity of matter in an object. It is a scalar quantity measured in kilograms (kg).
Weight is the gravitational force acting on an object with mass. It is a vector quantity measured in newtons (N).
Mass resists changes in motion; weight depends on the gravitational field strength.

Which of the following statements about mass and weight is correct?

Weight is measured in kilograms
Mass = weight × gravitational field strength
Weight is measured in newtons
Mass is a force

Weight & Gravitational Field Strength

Gravitational field strength (g) is the force per unit mass acting on an object in a gravitational field.
On Earth, g = 9.8 N/kg. The equation linking weight, mass and g is: W = m × g.
An object's mass is constant everywhere; its weight changes with location because g changes.

An astronaut has a mass of 75 kg on Earth. On the Moon, g = 1.6 N/kg. The astronaut's mass on the Moon is ____ kg and weight is ____ N.

Density

Density is the mass per unit volume of a material: ρ = m / V.
Units: kg/m³ or g/cm³. 1 g/cm³ = 1000 kg/m³.
Low-density materials have low mass for a given volume; high-density materials have high mass.

A paving slab has mass 73 kg and dimensions 0.04 m × 0.5 m × 0.85 m. What is its density in kg/m³?

4300
4294
0.017
73

Measuring Density of Regular Objects

Use a digital balance to measure mass.
Measure dimensions (length, width, height, radius) with a ruler, vernier calipers, or micrometer.
Calculate volume using the appropriate formula (e.g., V = l × w × h for a rectangular prism).
Repeat measurements and take averages to reduce random errors.

Which of these are true about measuring density of a regular object?

Mass is measured using a digital balance.
Volume is found by displacement of water.
Dimensions are measured with a ruler or calipers.
Repeat readings are not necessary.

Measuring Density of Irregular Objects

Use a eureka (displacement) can filled with water just below the spout.
Lower the object gently into the can; collect displaced water in a measuring cylinder.
The volume of displaced water equals the volume of the object.
Measure mass with a digital balance, then calculate density using ρ = m/V.

A student places an irregular stone in a eureka can. 20 cm³ of water is displaced. The stone's mass is 50 g. What is its density?

2.5 g/cm³
0.4 g/cm³
1000 g/cm³
70 g/cm³

Measuring Density of Liquids

Place an empty measuring cylinder on a digital balance and record its mass.
Add a known volume of liquid and record the new mass.
Mass of liquid = (mass of cylinder + liquid) – mass of empty cylinder.
Calculate density using ρ = mass of liquid / volume.

An empty measuring cylinder has mass 50 g. After adding 100 cm³ of liquid, total mass is 130 g. The mass of liquid is ____ g and its density is ____ g/cm³.

Floating & Sinking

An object floats if its density is less than the fluid's density; it sinks if denser.
Upthrust is an upward force on an object in a fluid, opposing weight.
If upthrust equals weight, the object floats; if upthrust < weight, it sinks.

A block of wood (density 0.9 g/cm³) is placed in water (density 1.0 g/cm³). What happens?

It sinks because it is denser than water.
It floats because it is less dense than water.
It floats because its density equals water's density.
It sinks because its density is less than water's.

Floating Liquids (Extended)

If two immiscible liquids are placed together, the less dense liquid floats on top.
Example: oil (density 0.8 g/cm³) floats on water (density 1.0 g/cm³).
This principle is used to store reactive metals like potassium in mineral oil.

Which of these are true about floating?

A liquid with lower density floats on a higher density liquid if they do not mix.
An object denser than the fluid will float.
Upthrust always acts downward.
If upthrust equals weight, the object floats.

Unlock all 40 questions, slides & more

Create a free account to see every question, the slides, flashcards and revision notes for this topic.

Past papers

Past-paper practice for this topic is coming soon.

🗂️ Coming soon