Mass and weight

Physics· Unit 3: Dynamics, Subtopic 5· 15 min read

1. Definitions and Core Differences★☆☆☆☆⏱ 5 min

📘 Definition

Mass

$m$

An intrinsic property of an object that measures the amount of matter it contains. It is a scalar quantity and constant regardless of location.

Example:

A 3 kg bowling ball has the same mass on Earth and the Moon.

📘 Definition

Weight

$W$

The gravitational force acting on an object's mass. It is a vector quantity that points towards the centre of the local gravitational field.

Example:

A 3 kg ball weighs ~29.4 N on Earth but only ~4.8 N on the Moon.

The most common mistake in CIE exams is treating these two quantities as interchangeable. Mass is a property of the object, weight is a force that depends on the local gravity.

📐 Worked Example

A student measures a stone's mass as 4.5 kg on Earth. What are the mass and weight of the stone on the Moon, where $g = 1.6 N kg^{- 1}$ ?

1
Mass is intrinsic, so it does not change with location:
2
$\text{Mass} = 4.5 \text{ kg}$
3
Weight is calculated using the formula $W = m g$ :
4
$W = (4.5 \text{ kg})(1.6 \text{ N kg}^{-1}) = 7.2 \text{ N}$
5
Final answer: mass = 4.5 kg, weight = 7.2 N towards the Moon's centre.

Exam tip:

Always check units: mass is in kilograms (kg), weight is in newtons (N), marks are often awarded for correct units.

2. Gravitational Field Strength and Weight Calculations★★☆☆☆⏱ 5 min

📘 Definition

Gravitational Field Strength

$g$

The gravitational force per unit mass acting on any object placed at a point in a gravitational field. Its unit is $N kg^{- 1}$ , equivalent to $m s^{- 2}$ .

Example:

On Earth's surface, $g \approx 9.8 N kg^{- 1}$ for CIE calculations.

Rearranging the definition $g = \frac{W}{m}$ gives the standard formula for weight: $W = m g$ . This formula is used in almost all dynamics problems, from projectile motion to equilibrium.

📐 Worked Example

A hiker has a weight of 735 N on Earth, where $g = 9.8 N kg^{- 1}$ . What is their weight on Venus, where $g = 8.9 N kg^{- 1}$ ?

1
First calculate the hiker's constant mass from Earth weight:
2
$m = \frac{W_{\text{Earth}}}{g_{\text{Earth}}} = \frac{735}{9.8} = 75 \text{ kg}$
3
Use the constant mass to calculate weight on Venus:
4
$W_{\text{Venus}} = m g_{\text{Venus}} = 75 \times 8.9 = 667.5 \text{ N} \approx 670 \text{ N (2 s.f.)}$

✓ Quick check

Check your understanding:

What is the correct unit for weight in CIE A-Level Physics?
- kg
- N
- N kg⁻¹
- m s⁻²
Reveal answer
1 —
Correct! Weight is a force, so its unit is the newton (N).

3. Inertial vs Gravitational Mass★★★☆☆⏱ 5 min

Mass can be classified by the property it measures. For CIE A-Level, you only need to know the basic distinction between the two types, which are experimentally shown to be equivalent.

📘 Definition

Inertial Mass

A measure of an object's resistance to acceleration when an external force is applied. It is defined from Newton's Second Law as $m_{i} = \frac{F}{a}$ .

📘 Definition

Gravitational Mass

A measure of how much gravitational force an object experiences in a given gravitational field. It determines weight via $W = m_{g} g$ .

📐 Worked Example

A 12 N force accelerates an object at $3.0 m s^{- 2}$ . What is the object's inertial mass, and what is its weight on Earth ( $g = 9.8 N kg^{- 1}$ )?

1
Calculate inertial mass from Newton's Second Law $F = ma$ :
2
$m_i = \frac{F}{a} = \frac{12}{3.0} = 4.0 \text{ kg}$
3
Since inertial mass = gravitational mass for all objects, calculate weight:
4
$W = m g = 4.0 \times 9.8 = 39.2 \text{ N}$

Exam tip:

If asked to distinguish the two, remember: inertial mass resists acceleration, gravitational mass interacts with gravity.

4. Common Pitfalls

Wrong move:

Claiming weight is a scalar quantity like mass

Why:

Weight is a force, which always has direction (towards the centre of mass of the gravitational source), so it is a vector

Correct move:

Always state that mass is scalar and weight is a vector force when asked to compare them

Wrong move:

Changing mass when calculating weight on another planet

Why:

Mass is an intrinsic property of the object that does not depend on location

Correct move:

Keep mass constant, only recalculate weight using the new local value of $g$

Wrong move:

Writing the unit of mass as N or weight as kg

Why:

CIE examiners consistently award and deduct marks for correct units, this is an easy mistake to avoid

Correct move:

Memorise: mass = kilogram (kg), weight = newton (N)

Wrong move:

Mixing up inertial and gravitational mass definitions in exams

Why:

Students often confuse which type of mass relates to acceleration vs gravity

Correct move:

Remember: INertial = INertia (resistance to acceleration), G Ravitational = G Ravity

5. Quick Reference Cheatsheet

Quantity	Symbol	Type	Unit	Key Property
Mass	$m$	Scalar	kg	Constant, intrinsic property
Weight	$W$	Vector	N	Depends on local $g$
Gravitational field strength	$g$	Scalar	N kg⁻¹	Force per unit mass
Inertial mass	$m_{i}$	Scalar	kg	Measures resistance to acceleration
Gravitational mass	$m_{g}$	Scalar	kg	Measures gravitational interaction
Weight formula			$W = m g$

6. Frequently Asked

Why is weight a vector but mass is scalar?

Mass only has magnitude, it is an amount of matter. Weight is a force that acts towards the centre of a gravitational field, so it has both magnitude and direction, making it a vector.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 12
MCQ comparing mass and weight
2023 · 21
Calculate weight on another planet

Going deeper

SyllabusOfficial CIE 9702 Physics SyllabusCheck for latest syllabus updates

What's Next

Now that you understand the core difference between mass and weight, you are ready to build on this foundation for more advanced dynamics concepts. All of Newton's laws of motion rely on the correct distinction between mass (an intrinsic property) and weight (a gravitational force), and you will use the formula $W = m g$ in almost every subsequent topic, from projectile motion and equilibrium to circular motion and gravitation. Getting this concept right early helps you avoid losing easy marks in both multiple choice and written paper questions, where this distinction is frequently tested.