IGCSE Physics | Practice Test — Answers & Worked Solutions
Write down the definition of mass.
Mass is the amount of matter in an object, measured relative to the observer when the object is at rest.
Write down the definition of weight.
Weight is the gravitational force acting on an object that has mass.
State the unit of mass and the unit of weight.
Write down the equation for gravitational field strength $g$. Define each symbol and state its unit.
- $g$ = gravitational field strength — unit: N/kg
- $W$ = weight — unit: N
- $m$ = mass — unit: kg
State the approximate value and unit of gravitational field strength at the surface of the Earth.
Apart from being a measure of force per unit mass, what else does $g$ represent in terms of motion?
$g$ is also equal to the acceleration of free fall.
An object is taken from Earth to the Moon. What happens to its mass? Explain your answer.
The mass does not change.
An object is taken from Earth to the Moon. What happens to its weight? Explain your answer.
The weight decreases.
Name one piece of equipment used to compare the masses of two objects.
Define what is meant by a gravitational field. Supplement
A gravitational field is a region of space where a mass experiences a force due to gravity.
A bag has a mass of 4 kg. Calculate its weight on Earth. ($g = 9.8\ \text{N/kg}$)
- Formula: $$W = m \times g$$
- Given: $m = 4\ \text{kg}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$W = 4 \times 9.8$$
- Arithmetic: $4 \times 9.8 = 4 \times (10 – 0.2) = 40 – 0.8 = 39.2$
- Answer: $$W = 39.2\ \text{N}$$
An object weighs 19.6 N on Earth ($g = 9.8\ \text{N/kg}$). Calculate its mass.
- Formula: $$g = \frac{W}{m} \implies m = \frac{W}{g}$$
- Given: $W = 19.6\ \text{N}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$m = \frac{19.6}{9.8}$$
- Check: $9.8 \times 2 = 19.6$ ✓
- Answer: $$m = 2\ \text{kg}$$
A rock weighs 98 N on Earth ($g = 9.8\ \text{N/kg}$). Calculate the mass of the rock.
- Formula: $$m = \frac{W}{g}$$
- Given: $W = 98\ \text{N}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$m = \frac{98}{9.8}$$
- Check: $9.8 \times 10 = 98$ ✓
- Answer: $$m = 10\ \text{kg}$$
An astronaut has a mass of 60 kg. Calculate their weight on the Moon, where $g = 1.6\ \text{N/kg}$.
- Formula: $$W = m \times g$$
- Given: $m = 60\ \text{kg}$, $g = 1.6\ \text{N/kg}$
- Substitute: $$W = 60 \times 1.6$$
- Arithmetic: $60 \times 1.6 = 60 \times 1 + 60 \times 0.6 = 60 + 36 = 96$
- Answer: $$W = 96\ \text{N}$$
A probe has a mass of 3 kg. Calculate its weight on Mars, where $g = 3.7\ \text{N/kg}$.
- Formula: $$W = m \times g$$
- Given: $m = 3\ \text{kg}$, $g = 3.7\ \text{N/kg}$
- Substitute: $$W = 3 \times 3.7$$
- Arithmetic: $3 \times 3.7 = 3 \times 3 + 3 \times 0.7 = 9 + 2.1 = 11.1$
- Answer: $$W = 11.1\ \text{N}$$
An object weighs 44.1 N on Earth ($g = 9.8\ \text{N/kg}$).
(a) Calculate the mass of the object. (b) Calculate the weight of the object on the Moon ($g = 1.6\ \text{N/kg}$).
- Formula: $$m = \frac{W}{g}$$
- Given: $W = 44.1\ \text{N}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$m = \frac{44.1}{9.8}$$
- Check: $9.8 \times 4 = 39.2$; $9.8 \times 0.5 = 4.9$; $39.2 + 4.9 = 44.1$ ✓ so $m = 4.5$
- Answer: $$m = 4.5\ \text{kg}$$
- Formula: $$W = m \times g$$
- Given: $m = 4.5\ \text{kg}$, $g = 1.6\ \text{N/kg}$
- Substitute: $$W = 4.5 \times 1.6$$
- Arithmetic: $4 \times 1.6 = 6.4$; $0.5 \times 1.6 = 0.8$; $6.4 + 0.8 = 7.2$
- Answer: $$W = 7.2\ \text{N}$$
Two objects are placed on a beam balance. Object A has a mass of 500 g. Object B also has a mass of 500 g.
(a) What does the balance show on Earth? (b) The same experiment is repeated on the Moon. What does the balance show? Explain why.
The balance is level (balanced). Both objects have equal mass, so equal gravitational force acts on each side.
The balance is still balanced.
A beam balance compares masses by comparing the gravitational force on each side. On the Moon, $g$ is smaller — but it is the same $g$ acting on both sides. The ratio of forces is unchanged, so the balance still reads level.
A space probe on the Moon has a weight of 24 N ($g_\text{Moon} = 1.6\ \text{N/kg}$).
(a) Calculate the mass of the probe. (b) Calculate the weight of the probe on Earth ($g = 9.8\ \text{N/kg}$).
- Formula: $$m = \frac{W}{g}$$
- Given: $W = 24\ \text{N}$, $g = 1.6\ \text{N/kg}$
- Substitute: $$m = \frac{24}{1.6}$$
- Arithmetic: $1.6 \times 10 = 16$; $1.6 \times 5 = 8$; $16 + 8 = 24$ ✓ so $m = 15$
- Answer: $$m = 15\ \text{kg}$$
- Formula: $$W = m \times g$$
- Given: $m = 15\ \text{kg}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$W = 15 \times 9.8$$
- Arithmetic: $15 \times 10 = 150$; $15 \times 0.2 = 3$; $150 – 3 = 147$
- Answer: $$W = 147\ \text{N}$$
Calculate the weight of a 25 kg object on a planet where $g = 12\ \text{N/kg}$.
- Formula: $$W = m \times g$$
- Given: $m = 25\ \text{kg}$, $g = 12\ \text{N/kg}$
- Substitute: $$W = 25 \times 12$$
- Arithmetic: $25 \times 12 = 25 \times 10 + 25 \times 2 = 250 + 50 = 300$
- Answer: $$W = 300\ \text{N}$$
A student’s weight on Earth is 637 N ($g = 9.8\ \text{N/kg}$). Calculate their mass.
- Formula: $$m = \frac{W}{g}$$
- Given: $W = 637\ \text{N}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$m = \frac{637}{9.8}$$
- Arithmetic: $9.8 \times 60 = 588$; $9.8 \times 5 = 49$; $588 + 49 = 637$ ✓ so $m = 65$
- Answer: $$m = 65\ \text{kg}$$
An astronaut has a mass of 80 kg.
(a) Calculate the astronaut’s weight on Earth ($g = 9.8\ \text{N/kg}$).
(b) Calculate the astronaut’s weight on the Moon ($g = 1.6\ \text{N/kg}$).
(c) The astronaut is weighed using a beam balance on the Moon. Will the reading be different from on Earth? Explain your answer.
- Formula: $$W = m \times g$$
- Given: $m = 80\ \text{kg}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$W = 80 \times 9.8$$
- Arithmetic: $80 \times 10 = 800$; $80 \times 0.2 = 16$; $800 – 16 = 784$
- Answer: $$W = 784\ \text{N}$$
- Formula: $$W = m \times g$$
- Given: $m = 80\ \text{kg}$, $g = 1.6\ \text{N/kg}$
- Substitute: $$W = 80 \times 1.6$$
- Arithmetic: $80 \times 1 = 80$; $80 \times 0.6 = 48$; $80 + 48 = 128$
- Answer: $$W = 128\ \text{N}$$
The beam balance will show the same reading — 80 kg.
A beam balance works by comparing the gravitational force on both sides. On the Moon, $g$ is smaller, but it acts equally on both sides. The ratio of forces is the same, so the balance is still level at 80 kg.
A student makes the following statement: “My mass is 50 kg on Earth. So on the Moon my mass must be less, because the Moon’s gravity is weaker.”
(a) Identify and explain the scientific error. (b) Calculate the student’s weight on Earth ($g = 9.8\ \text{N/kg}$). (c) Calculate the student’s weight on the Moon ($g = 1.6\ \text{N/kg}$).
The student is confusing mass with weight. Mass does not change with location — it is the amount of matter in the object. Only weight changes, because weight depends on the gravitational field strength ($g$), which is different on the Moon.
- Formula: $$W = m \times g$$
- Given: $m = 50\ \text{kg}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$W = 50 \times 9.8$$
- Arithmetic: $50 \times 10 = 500$; $50 \times 0.2 = 10$; $500 – 10 = 490$
- Answer: $$W = 490\ \text{N}$$
- Formula: $$W = m \times g$$
- Given: $m = 50\ \text{kg}$, $g = 1.6\ \text{N/kg}$
- Arithmetic: $50 \times 1.6 = 80$
- Answer: $$W = 80\ \text{N}$$
An object has a weight of 78.4 N on Earth ($g = 9.8\ \text{N/kg}$).
(a) Calculate the mass of the object.
(b) Calculate the weight on a planet where $g = 6.2\ \text{N/kg}$.
(c) Explain, using the concept of gravitational field strength, why the weight is different. Supplement
- Formula: $$m = \frac{W}{g}$$
- Given: $W = 78.4\ \text{N}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$m = \frac{78.4}{9.8}$$
- Check: $9.8 \times 8 = 78.4$ ✓
- Answer: $$m = 8\ \text{kg}$$
- Formula: $$W = m \times g$$
- Given: $m = 8\ \text{kg}$, $g = 6.2\ \text{N/kg}$
- Arithmetic: $8 \times 6 = 48$; $8 \times 0.2 = 1.6$; $48 + 1.6 = 49.6$
- Answer: $$W = 49.6\ \text{N}$$
Weight is the force that a gravitational field exerts on a mass. The stronger the gravitational field, the greater the force on the same mass.
This planet has $g = 6.2\ \text{N/kg}$, which is less than Earth’s $g = 9.8\ \text{N/kg}$. Its gravitational field is weaker, so it exerts a smaller force on the object. Since $W = m \times g$ and $g$ is smaller, the weight is smaller.
Supplement
(a) State what a gravitational field is and describe how it affects a mass placed within it.
(b) Explain how weight is the effect of a gravitational field on a mass.
(c) An object of mass 2 kg is taken to deep space where $g \approx 0\ \text{N/kg}$. State its weight and whether its mass has changed. Explain.
A gravitational field is a region of space where a mass experiences a gravitational force. Any object with mass creates a gravitational field around it. A mass placed inside this field will feel a pull towards the source of gravity.
When a mass is placed inside a gravitational field, the field exerts a force on it. This force is what we call weight. The stronger the gravitational field (higher $g$), the greater the force on the mass, and therefore the greater the weight.
Weight: In deep space, $g \approx 0\ \text{N/kg}$, so:
$$W = m \times g = 2 \times 0 = 0\ \text{N}$$Mass: The mass is still 2 kg. Mass is the amount of matter in the object — it does not depend on gravity. Only weight changes.
A new planet is discovered with $g = 4.9\ \text{N/kg}$. A probe of mass 200 kg is sent to this planet. Supplement
(a) Calculate the weight of the probe on the new planet.
(b) Calculate the weight of the probe on Earth ($g = 9.8\ \text{N/kg}$).
(c) A scientist uses a beam balance to measure a rock on this planet. It reads 5 kg. What would the rock’s mass be on Earth? Explain.
- Formula: $$W = m \times g$$
- Given: $m = 200\ \text{kg}$, $g = 4.9\ \text{N/kg}$
- Substitute: $$W = 200 \times 4.9$$
- Arithmetic: $200 \times 5 = 1000$; $200 \times 0.1 = 20$; $1000 – 20 = 980$
- Answer: $$W = 980\ \text{N}$$
- Formula: $$W = m \times g$$
- Given: $m = 200\ \text{kg}$, $g = 9.8\ \text{N/kg}$
- Substitute: $$W = 200 \times 9.8$$
- Arithmetic: $200 \times 10 = 2000$; $200 \times 0.2 = 40$; $2000 – 40 = 1960$
- Answer: $$W = 1960\ \text{N}$$
The rock’s mass on Earth is still 5 kg.
A beam balance compares masses. It gives the correct mass reading regardless of the gravitational field strength, because both sides of the balance experience the same $g$. Mass does not change with location — so a rock that has a mass of 5 kg on the new planet also has a mass of 5 kg on Earth.
