Thirty Questions. Thirty Minutes. Go.

Section 14 taught you the fast way through this chapter — the verbatim statements the paper asks for word for word, the recognition table of every formula with a hook attached, the single-step numericals, the rankings on YY, BB and compressibility, the loaded-wire and ocean-depth templates, the graph readings, the two special formats and the elimination habits. This section finds out whether any of it survives contact with a clock.

There is no new physics below. There are 30 questions built the way this paper builds them, and one rule that matters more than the rest: you are being tested on pace, not on cleverness. If a question here takes you four lines of algebra, you have misread it.

How to attempt this set

Key Point: Blank sheet, pen, timer. Attempt all 30 questions in one unbroken sitting, and do not read a single explanation until your last answer is written. A drill you pause to check is a reading exercise, and reading exercises do not build speed.

The setup What it is
Number of questions 30, single correct option
Marking scheme +4+4 correct, 1-1 incorrect, 00 unattempted
Maximum score 30×4=12030 \times 4 = 120 marks
Minimum possible score 30×(1)=3030 \times (-1) = -30 marks
Suggested time limit 30 minutes (45 Physics questions in about 45 minutes, so roughly a minute each)
Take gg as 9.8 m/s2^2 throughout. No question here uses 10
Allowed a rough sheet and your memory
Not allowed calculator, formula sheet, or a glance back at the earlier sections

The constants sheet

Every question that needs a number uses these and no others.

Quantity Value
YY steel 2.0×10112.0 \times 10^{11} Pa
YY copper 1.2×10111.2 \times 10^{11} Pa
YY aluminium 0.70×10110.70 \times 10^{11} Pa
GG steel 0.84×10110.84 \times 10^{11} Pa
BB steel 1.6×10111.6 \times 10^{11} Pa
BB copper 1.4×10111.4 \times 10^{11} Pa
BB water 2.2×1092.2 \times 10^{9} Pa
compressibility of water 4.5×10104.5 \times 10^{-10} Pa1^{-1}
density of sea water 1030 kg/m3^3
α\alpha for steel 1.2×1051.2 \times 10^{-5} per degree Celsius
Poisson's ratio of steel about 0.300.30
Useful values π=3.14\pi = 3.14, 3=1.73\sqrt{3} = 1.73, tan45°=1\tan 45° = 1

Two housekeeping notes on those. Every ocean-depth question here uses the gauge pressure ρgh\rho gh and ignores the atmosphere, which would add only 1.013×1051.013 \times 10^{5} Pa — well under one per cent at any depth asked about. And σ\sigma means Poisson's ratio throughout; stress is written FA\frac{F}{A}, strain is ε\varepsilon, and the moduli are YY, GG and BB with k=1Bk = \frac{1}{B}.

[Important] The 30-minute limit is the entire exercise. Most students can get 27 of these right given an hour — and an hour is exactly what the real paper will not give you. Finishing in 30 minutes with 24 correct puts you in far better shape than taking 55 minutes to get 27. Keep the timer where you can see it, and the moment a question passes 60 seconds, mark your best surviving option and move on.

Here is the arithmetic that makes that instruction safe. A blind guess among four options is worth 434=+0.25\frac{4-3}{4} = +0.25, essentially nothing. But once you have eliminated two options, a guess between the survivors is worth 412=+1.5\frac{4-1}{2} = +1.5 marks on average. Eliminate first, then commit. Leave blank only what you could not narrow down at all.

What this set covers

Topic map, marking scheme and constants sheet for the 30-question drill

Topic Questions How many
Stress and strain Q1 to Q3 3
Hooke's law and the stress-strain curve Q4 to Q6 3
Young's modulus and the loaded wire Q7 to Q12 6
Shear modulus Q13 to Q15 3
Bulk modulus and compressibility Q16 to Q19 4
Poisson's ratio and the elastic constants Q20 to Q21 2
Strain energy Q22 to Q23 2
Thermal stress Q24 1
Engineering applications Q25 1
Assertion-reason Q26 to Q28 3
Column matching Q29 to Q30 2

That weighting is not arbitrary — it is how this paper actually samples the chapter. Young's modulus is 6 of the 30, because the loaded wire is the single most reliably repeated set-up here and each question is worth a whole mark in half a minute once the four-line template is automatic. The last five drill the two formats this paper uses and the engineering papers do not: three assertion-reason items and two column matches. If you have never sat one of those under time pressure, they are the questions most likely to cost you marks.

[Important] Notice what is not in this set. No integration over a tapering bar, no rotating rod, no rigid-bar-on-three-wires compatibility, no dropped-mass dynamic extension, no torsional oscillation. Those live in Section 12. Every question below can be finished with one formula card, one definition, or one line of arithmetic. If you find yourself wanting calculus, you are solving a question that is not on this page.

The difficulty mix is deliberately calibrated: roughly 35% easy, 45% medium and 20% hard.

Mark It Honestly, Then Read Your Own Answer Sheet

Score with the real scheme: +4+4 for every correct answer, 1-1 for every wrong one, 00 for every blank. No half marks for "I nearly had that one". The number you end up with is the number that means something.

Pacing line for the drill beside the four self-scoring bands

The bands

Your score (out of 120) Verdict What to do next
100 to 120 Exam ready. Over 80% on a full-length set, inside the time. This chapter is now free marks for you. Revisit only the items you missed, then move to the next chapter.
78 to 99 Fast but leaky. You know the material; something leaks on the way to the answer sheet. Almost always a diameter used as a radius or an area left in mm2^2, not a gap in knowledge. Redo every wrong question without the explanation first, and count how many you fix alone.
48 to 77 Recall gaps. The speed is not the problem; the lookup is. Go back to Section 14's recognition table and unit card — stress and moduli in pascal, strain with no unit, compressibility in Pa1^{-1}, energy density in J/m3^3 — and learn them as flashcards. Then re-attempt this set cold.
Below 48 Rebuild first. Work Sections 1 to 10 properly, then Section 11's worked problems, then Section 14. Re-attempting this set today would teach you nothing except the answer key.

Sort your mistakes into three piles

Do this before you read a single explanation. It is the most useful ten minutes in this section.

  1. Did not know it. A formula you could not recall, a unit you had never learnt precisely, which modulus belongs to which deformation. Cheapest to fix — it is a memory job, and it takes an evening.
  2. Knew it, computed it wrong. You used the diameter where the radius belonged, left an area in mm2^2, dropped the factor of one half in the energy, or forgot to multiply the strain back by the length. Slow down for four seconds on the final line.
  3. Knew it, answered a different question. You gave the stress when it asked for the strain; the breaking load when it asked for the breaking stress; the volume change of the water when it asked about the steel ball in it. The distractors here are built specifically to reward this mistake.

Key Point: Two students both score 88. The first has four pile-1 mistakes and a syllabus gap that revision closes in a day. The second has nine pile-3 mistakes and a reading habit that will follow them into the exam hall. Pile 3 is the expensive one — count it before you explain it away.

The ten recall facts this set keeps testing

  • Stress is the internal restoring force per unit area, in pascal, with dimensions [ML1T2][ML^{-1}T^{-2}] — the same as pressure, and yet not pressure, because stress is not a vector.
  • Strain is a fractional change in a dimension: no unit, no dimensions. So is Poisson's ratio.
  • The three pairs: longitudinal stress with ΔLL\frac{\Delta L}{L} and modulus YY; shearing stress with θ\theta and modulus GG; hydraulic stress Δp\Delta p with ΔVV\frac{\Delta V}{V} and modulus BB. Shear changes shape not volume; hydraulic changes volume not shape.
  • Y=FLAΔLY = \frac{FL}{A\,\Delta L}, so ΔL=FLAYLr2Y\Delta L = \frac{FL}{AY} \propto \frac{L}{r^{2}Y}, and a stretched wire is a spring of force constant k=YALk = \frac{YA}{L}.
  • G=FAθG = \frac{F}{A\theta}, with AA the face the force slides along and θ\theta the slip divided by the distance to the fixed face.
  • B=ΔpΔV/VB = -\frac{\Delta p}{\Delta V/V}, the minus sign there to make BB positive, and k=1Bk = \frac{1}{B} in Pa1^{-1}. Only BB exists for a liquid or a gas, and isothermally a gas has B=pB = p.
  • σ=Δd/dΔL/L\sigma = -\frac{\Delta d/d}{\Delta L/L}, bounded by 1σ0.5-1 \le \sigma \le 0.5, and ΔVV=(12σ)ΔLL\frac{\Delta V}{V} = (1-2\sigma)\frac{\Delta L}{L}, which is zero at σ=0.5\sigma = 0.5.
  • U=12FΔLU = \frac{1}{2}F\,\Delta L and u=12×u = \frac{1}{2}\times stress ×\times strain =12Yε2=(F/A)22Y= \frac{1}{2}Y\varepsilon^{2} = \frac{(F/A)^{2}}{2Y}. The one half is not optional.
  • Thermal stress in a clamped rod is YαΔTY\alpha\,\Delta T, independent of both the length and the cross-section.
  • Steel is more elastic than rubber, because more elastic means a larger modulus. Breaking stress is a material property and does not depend on the length of the wire.

One more pass, then move on

Every question below has a full step-by-step explanation and a note on why each wrong option is tempting. Read the explanation even for the questions you got right — on a paper this tight, the difference between a 20-second method and a 70-second method decides whether you finish Physics at all.

[Important] When you are done, do not immediately re-attempt the set. You would be scoring your memory of the answer key, not your physics. Leave it a week, then sit it again cold with the same 30-minute timer. The second score is the honest one.