Physics 9702 · syllabus 4
Cambridge A Level Physics 9702 — Forces, density and pressure topical past papers
Turning effects and the equilibrium of forces, couples and centre of gravity, and how density and pressure in a fluid give rise to upthrust.
- Questions
- 568
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 143
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What Forces, density and pressure covers
This topic asks when an object stays still. The moment of a force about a point is the force multiplied by the perpendicular distance from the point to its line of action. A couple, two equal and opposite forces that do not act along the same line, turns an object without moving it along, and its torque is one force times the perpendicular distance between them. An object's weight can be taken to act at its centre of gravity, so a uniform beam's weight acts at its midpoint.
An object is in equilibrium when there is neither a resultant force nor a resultant torque on it. The principle of moments deals with turning, and for three coplanar forces in equilibrium a closed vector triangle deals with the rest: drawn head to tail, the forces return to their starting point. If the three forces are not parallel, their lines of action also pass through one point.
Density and pressure complete the topic. From their definitions you derive the hydrostatic pressure difference Δp = ρgΔh, and because pressure grows with depth, a fluid pushes harder on the bottom of a submerged object than on its top. That difference is the upthrust, F = ρgV, where ρ is the density of the fluid and V the volume displaced. This is AS content, examined on Papers 1 and 2.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 4 Forces, density and pressure
- 4.1 Turning effects of forces
- 4.2 Equilibrium of forces
- 4.3 Density and pressure
What you should be able to do
- Calculate moments and torques using the perpendicular distance to the line of action
- Apply the principle of moments to beams, levers and planks with more than one support
- Draw and use a closed vector triangle for three forces in equilibrium
- Derive Δp = ρgΔh from the definitions of density and pressure
- Explain upthrust as a difference in hydrostatic pressure and calculate it with F = ρgV
Key ideas
- Moment = F × d, where d is the perpendicular distance from the pivot to the line of action (N m)
- Torque of a couple = one of the forces × the perpendicular distance between them
- Equilibrium: no resultant force, and the sum of clockwise moments = the sum of anticlockwise moments about any point
- Density ρ = m/V (kg m⁻³); pressure p = F/A (Pa = N m⁻²)
- Hydrostatic pressure difference Δp = ρgΔh; upthrust F = ρgV, with ρ the density of the fluid
How Forces, density and pressure has been examined
From 2022 to 2026, Forces, density and pressure was on Paper 2 · AS Level Structured Questions in 8 of 11 exam series, worth about 13% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice | 112 | 9% | 11 of 11 |
| Paper 2 · AS Level Structured Questions | 28 | 13% | 8 of 11 |
| Paper 4 · A Level Structured Questions | 3 | 1% | 2 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1.
Filed in Momentum under: Forces, Density & Pressure.
A worked example
A wooden block of volume 2.0 × 10⁻³ m³ and density 800 kg m⁻³ is held completely under water by a string tied to the bottom of a tank. The density of water is 1000 kg m⁻³. Find the tension in the string.
- Weight of block: W = ρ(block) × V × g = 800 × 2.0 × 10⁻³ × 9.81 = 15.7 N
- Upthrust from the water displaced: F = ρ(water) × g × V = 1000 × 9.81 × 2.0 × 10⁻³ = 19.6 N
- The block is in equilibrium: upthrust (upwards) = weight + tension (both downwards)
- Tension = 19.6 − 15.7 = 3.9 N
Answer: 3.9 N
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Multiplying a force by the distance along a slanted beam instead of the perpendicular distance — for a force at angle θ to the beam, the moment is F × d sin θ
- Using the object's density in F = ρgV — upthrust depends on the density of the fluid displaced, not of the object
- Leaving the weight of a uniform beam out of the moments equation — it acts at the centre and often provides one of the largest moments
- Taking moments about a point other than where an unknown force acts, then struggling with two unknowns — a force through the chosen point has zero moment, which is why that point is chosen
- Adding atmospheric pressure when a pressure difference was asked for, or leaving it out when the total pressure at a depth was asked for
Exam technique
- Take moments about the point where an unknown force acts, so that force drops out of the equation
- When asked for the conditions for equilibrium, give both: no resultant force and no resultant moment
- Draw vector triangles to scale with a stated scale when a graphical answer is asked for, and label each side with its force
- Give moments and torques in N m, never N m⁻¹ or J
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.