Thirty Questions. Thirty Minutes. Go.

Section 13 taught you the fast way through this chapter — the verbatim statements the paper asks for word for word, the formula-recognition table, the single-step numericals, the gg-variation rankings, the satellite and escape-speed templates, the two special formats, 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
Gravitational constant GG 6.67×10116.67 \times 10^{-11} N m2^2/kg2^2
Earth's radius RER_E 6.4×1066.4 \times 10^{6} m, i.e. 6400 km
Surface gravity gg 9.8 m/s2^2
GME=gRE2GM_E = gR_E^2 4.01×10144.01 \times 10^{14} m3^3/s2^2
Escape speed from the surface vev_e 11.2 km/s
Orbital speed of a surface-skimming satellite vov_o 7.9 km/s
Gravitational potential at the surface 6.27×107-6.27 \times 10^{7} J/kg
Radius of the geostationary orbit 4.2×1074.2 \times 10^{7} m
Earth's angular speed of rotation ω\omega 7.29×1057.29 \times 10^{-5} rad/s
Useful roots 2=1.41\sqrt{2} = 1.41, 3=1.73\sqrt{3} = 1.73, π=3.14\pi = 3.14

These are internally consistent: 2gRE\sqrt{2gR_E} comes out at exactly 11 200 m/s, and 11.22=7.9\frac{11.2}{\sqrt2} = 7.9 km/s. Never mix 9.8 and 10 inside one problem — a 2% shift is enough to land you on the wrong option.

[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
Kepler's three laws Q1 to Q3 3
The universal law and the shell theorem Q4 to Q6 3
gg at the surface and its variation with altitude, depth and rotation Q7 to Q11 5
Gravitational potential energy and gravitational potential Q12 to Q14 3
Escape speed Q15 to Q17 3
Orbital speed and time period Q18 to Q20 3
Satellite energy and binding energy Q21 to Q22 2
Geostationary and polar satellites Q23 to Q24 2
Weightlessness 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. The variation of gg is 5 of the 30, because it is the most reliably repeated item here and each question is worth a whole mark in twenty seconds once the three formulae are in your head. 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 field or potential of an extended body by integration, no tunnel-through-the-Earth oscillation, no vis-viva relation, no Hohmann transfer, no binary stars, no gravitational self-energy. Those live in Section 11. 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 missing RER_E or a lost minus sign, not a gap. 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 15's cards — the gg-variation card, the UU-and-VV card, the escape-and-orbital card, the energy triple — and learn them as flashcards. Then re-attempt this set cold.
Below 48 Rebuild first. Work Sections 1 to 9 properly, then Section 10's worked problems, then Section 13. 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, the difference between what the first shell theorem says and what the second one says. Cheapest to fix — it is a memory job, and it takes an evening.
  2. Knew it, computed it wrong. You forgot to add RER_E to a height, you lost the factor 2 between GMmr\frac{GMm}{r} and GMm2r\frac{GMm}{2r}, or you left a bound orbit with a positive total energy. Slow down for four seconds on the final line.
  3. Knew it, answered a different question. You gave the potential when it asked for the potential energy; the total energy when it asked for the binding energy; the value at a height when it asked for the value at a depth. 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

  • Kepler's laws: an ellipse with the Sun at one focus; equal areas in equal times, which is angular momentum conserved; and T2a3T^2 \propto a^3, with aa the semi-major axis.
  • F=Gm1m2r2F = G\frac{m_1m_2}{r^2}, always attractive, always along the line joining the two bodies, and it obeys superposition — total force is the vector sum of the pairwise forces, each computed as though the others were absent.
  • The two shell theorems: a uniform shell pulls an outside point as though all its mass were at its centre, and exerts no force at all on an inside point. Inside a solid sphere only the mass beneath you counts, so grg \propto r.
  • g=GMERE2=43πGρREg = \frac{GM_E}{R_E^2} = \frac{4}{3}\pi G\rho R_E — use the first form when the mass is given, the second when the density is.
  • The three variations: gh=GME(RE+h)2g(12hRE)g_h = \frac{GM_E}{(R_E+h)^2} \approx g\left(1-\frac{2h}{R_E}\right) for small hh; gd=g(1dRE)g_d = g\left(1-\frac{d}{R_E}\right) exactly, for a uniform Earth; and gλ=gω2REcos2λg_\lambda = g - \omega^2R_E\cos^2\lambda, largest at the poles and smallest at the equator.
  • U=GMmrU = -\frac{GMm}{r} in joules, V=GMrV = -\frac{GM}{r} in J/kg, and U=mVU = mV. Both are negative, both are zero only at infinity, and both are scalars.
  • ve=2GMR=2gR=11.2v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR} = 11.2 km/s for the Earth, independent of the mass of the body, of its direction of projection and of its shape.
  • vo=GMrv_o = \sqrt{\frac{GM}{r}} and T=2πr3GMT = 2\pi\sqrt{\frac{r^3}{GM}}, so higher orbits are slower and take longer, and ve=2vov_e = \sqrt{2}\,v_o at the same radius.
  • For a circular orbit K=GMm2rK = \frac{GMm}{2r}, U=GMmrU = -\frac{GMm}{r}, E=GMm2rE = -\frac{GMm}{2r}, so E=KE = -K and U=2EU = 2E. The binding energy is +GMm2r+\frac{GMm}{2r}.
  • A geostationary satellite has a 24-hour period, orbits in the equatorial plane from west to east, and sits at 4.2×1074.2\times10^{7} m from the Earth's centre, about 36 000 km up. A polar satellite is low, quick, and sweeps the whole globe as the Earth turns beneath it.

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.