GAM · Hydrostatics — Strategy & Tricks

📐 The rules the pack always hands you

Hydrostatics in the GAM is not a physics test. It is a reading-and-substitution test that happens to be about liquids. Every pack states its own formula, density, g and often its atmospheric pressure — nothing is asked that the text did not supply. Your job, in ninety seconds: apply the stated relation without dropping a unit.

The format. About 60 questions in 90 minutes, roughly 90 seconds each. Four options, exactly one correct, no calculator. Packs are shared: one passage feeds four or five linked questions. No negative marking — a blank scores like a wrong answer, so every item gets an answer.

p = ρgh — gauge pressure at depth h
Δp = ρgΔh — only vertical separation counts
F = pA — pressure on a flat area
F_B = ρ_fluid·g·V_displaced — weight of displaced fluid
Floating: ρ_fluid·V_sub = m — g cancels
Pascal: F_out = F_in·(A_out/A_in)
p_abs = p_atm + p_gauge | ρ = m/V | W = mg

Pressure at depth. p = ρgh grows with depth and density and nothing else — width, shape and volume appear in no formula. Since 1,000 × 10 × 1 = 10,000 Pa, water gives 10 kPa per metre at g = 10. Force needs an area: F = pA, taking p at mid-depth on a vertical panel.

Buoyancy. The upward force equals the weight of the liquid pushed aside: F_B = ρ_fluid g V_displaced. Both symbols are bait: the density is the fluid's, never the object's; the volume is the displaced one, all of the object when held under, only the wet part when floating. Floating means buoyancy equals weight, so g cancels: ρ_fluid V_sub = m.

Pascal and the atmosphere. One pressure reaches both pistons of a confined fluid, so force scales with area. A gauge reads the pressure above atmospheric: p_abs = p_atm + p_gauge, and a pack that says 'absolute' always supplies p_atm, typically 100 kPa.

Units. Work in metres, cubic metres and kg/m³: cm ÷ 100, litres ÷ 1,000, g/cm³ × 1,000. Convert as you copy the number down, never mid-formula.

👀 Name the variant in five seconds

Before any arithmetic, name the variant — the nouns in the stem do it. Depth means substitution, displaces buoyancy, floats equilibrium, piston a ratio, absolute add the atmosphere. Naming it tells you which line to reread and what single unknown you are chasing.

Items arrive in linked groups — one pack, four or five questions, the later ones reusing earlier results, so each number goes into the margin once. About one per group is conceptual ('if the depth doubles…'): p is proportional to h, F_B to V, and a wider tank appears nowhere. Don't compute; read.

🧠 Numbers first, then the stem

Here is the habit that separates a 45-second item from a two-minute one: extract the givens before you read the question. Read the stem first and you go hunting back through the pack for a number, then substitute the wrong unit. Reversing the order removes the hunt and most of the errors.

1. Scan the pack for every number, each into the margin with its symbol and unit: ρ = 1,150 kg/m³, g = 10 m/s², h = 300 cm. Twenty seconds per group.
2. Convert on the spot. 300 cm becomes 3.0 m before it goes near a formula; 20 litres becomes 0.020 m³. Pick Pa or kPa and stay there.
3. Tag the relation. Underline the stated formula. Gauge or absolute? Which densities are given? If both, label them: one is bait.
4. Now read the stem, match its nouns to the variant, and write the unknown you need.
5. Read the options, then substitute — their spacing sets the precision required.
6. Check direction, then say the unit. Deeper is more pressure, denser fluid more buoyancy, the bigger piston more force.

Mini-example. That table sits in the pack, which also states g = 10 m/s² and p = ρgh. The stem: the gauge pressure 3.0 m below the surface of the brine? Numbers first — brine row, ρ = 1,150, h = 3.0 m; p = 1,150 × 10 × 3.0 = 34,500 Pa = 34.5 kPa. Read the row the stem names: petrol would give 22.5 kPa and water 30 kPa, and both wait in the options. The freezing-point column is there to slow you down.

✂️ Ratios, cancelled g, and 10 kPa per metre

The packs almost always hand you ρ = 1,000 kg/m³ and g = 10 m/s². That product, 10,000 newtons per cubic metre, is the only thing worth knowing cold.

Compute the change, not the totals. 'The tap moves from 2 m to 5 m' is 3 m × 10 kPa per metre = 30 kPa; 'density falls by 20%' means 80% of the old pressure. And cancel g wherever it stands on both sides: floating collapses to V_sub = m/ρ_fluid, the submerged fraction to ρ_object/ρ_fluid.

Layers add downward; panels average. Oil over water: the bottom pressure is the oil's ρgh plus the water's. A panel from 1.5 m to 3.5 m down averages at mid-depth 2.5 m, so 25 kPa × its area gives kilonewtons straight off.

⚡ Read the options before you compute

Two rules carry the pace. First, the pack's own definition answers every conceptual item. If it says buoyancy equals the weight of displaced liquid, then 'what does the buoyant force depend on?' is that sentence — displaced volume and fluid density — and every other option is noise.

Second, look at the options first. Ten times apart (2.5 / 25 / 250) asks only 'how many zeros?' Twenty per cent apart (25 / 30 / 35 / 40) wants the exact product, and the pack keeps the numbers round so you can get it. A pair differing by exactly 100 kPa is not arithmetic at all: it is asking gauge or absolute.

• Substitution (ρgh, pA, ρgV): 30–40 s.
• Conceptual (doubles, unchanged): 15–20 s.
• Inverse (depth or density): 40–50 s.
• Chained: 50–70 s, then 30 s per reuse.
• Inference (two readings): 75–90 s.

At 90 seconds a question, a five-item group is worth seven and a half minutes; numbers-first it takes four to five. The minutes you bank pay for the reading-heavy passages elsewhere in the module.

🪤 Where the wrong options come from

The wrong options are not random. Each is what one specific slip produces, so the four together map the mistakes the writers expect.

Two densities on the page means one is bait: weight uses the block's, buoyancy the liquid's, the fraction their ratio. Label them in the margin.

🧩 Worked examples: easy to hard

Each item is a miniature source pack with one question. Cover the steps, run the clock, then compare; the last step names the wrong options.

🎯 Recognition drills

Speed comes from recognition, not faster multiplication. Run these aloud, against the seconds shown.

🧭 Guided practice: one linked group

This is how the module serves hydrostatics: one pack, five questions, each leaning on the last. Work it against a watch, then tick the checklist.

1. Extract (20 s). ρ = 1,000, g = 10, p_atm = 100 kPa, h = 4 m, V = 0.016 m³, m = 14 kg.
2. Gauge pressure at the sensor (25 s). 4 m × 10 kPa per metre = 40 kPa — say the prefix, since 4 and 400 kPa are both offered.
3. Absolute pressure there (20 s). The word is in the stem: 100 + 40 = 140 kPa.
4. Weight and buoyancy (40 s). W = 14 × 10 = 140 N; F_B = 10,000 × 0.016 = 160 N. Both into the margin.
5. Net force, then a move to 6 m (45 s). 160 N up against 140 N down leaves 20 N upward, so the block rises. At 6 m the sensor reads 60 kPa, but F_B is still 160 N — the formula has no h in it.

• Numbers in the margin, with units, before the first stem.
• cm and litres converted before substituting.
• 'Gauge' or 'absolute' circled wherever the stem says either.
• Fluid density for buoyancy, object density for weight.
• Shared numbers computed once, then reused.

📈 Progressive practice

Untimed, one tier at a time. After each item, name the variant and the slip behind each wrong option; move up only when you can do that for all six unaided.

Easy: one formula, numbers straight from the pack, options ten times apart. Units and zeros are the job.

Easy — direct substitution and definitions → 6 real easy questions · free, no login

Medium: two steps chained — weight then buoyancy, oil then water — or a ratio. Options sit closer, so the product must be exact.

Medium — linked groups, ratios and stacked layers → 6 real medium questions · free, no login

Hard: the unknown is a density or a depth, the readings may carry an offset, or the question is whether the block floats at all. Work from differences.

Hard — inference, thresholds and pressure matching → 6 real hard questions · free, no login

⏱️ Speed training

Now the watch. Targets: 35 s easy, 55 s medium, 80 s hard — under the module's 90-second average, because you want this family to bank time.

1. Rung 1 — accuracy, no clock. Six items with the method written out; repeat until six of six are right.
2. Rung 2 — target pace. The same tier against the targets above. For every item over target, name the step that ate the seconds — extraction, conversion, arithmetic, options — and drill it alone.
3. Rung 3 — mixed and tight. Tiers shuffled at 45 seconds flat.

Easy sprint — 35 s per item → 6 real easy questions, against the clock · free, no login

Medium sprint — 55 s per item → 6 real medium questions, against the clock · free, no login

Hard sprint — 80 s per item → 6 real hard questions, against the clock · free, no login

🏆 Exam application

Hydrostatics arrives as one or two packs inside the 60-question paper, alongside research methods, vectors and inventory models — the most formulaic family there, and the one where a routine buys both marks and minutes.

1. Read the pack once, pen moving (20 s). Every number to the margin with its unit; underline the formula; note gauge or absolute and which densities you were given.
2. Glance at all the stems (10 s). Spot the chain, and take the conceptual item first — it is free.
3. Answer in order, options first (25–70 s each). Let their spacing set your precision, compute once, say the unit, mark. Naming one wrong option — 'that is the cm-as-m answer' — confirms your own choice.
4. Last thirty seconds: stop solving and sweep for blanks. With no negative marking, a reckoner-sized guess beats an empty box.

Exam simulation — medium, 60 s per item → 6 real medium questions, against the clock · free, no login

Exam simulation — hard, 75 s per item → 6 real hard questions, against the clock · free, no login

📋 Cheat sheet

p = ρgh | Δp = ρgΔh (vertical separation only)
F = pA | vertical panel: p at mid-depth × area
F_B = ρ_fluid·g·V_displaced (fluid density, displaced volume)
Floating: ρ_fluid·V_sub = m | fraction = ρ_object/ρ_fluid
Net force = F_B − W | W_app = W − F_B | W = mg
Hydraulic: F_out = F_in·(A_out/A_in) | layers: add ρgh downward
p_abs = p_atm + p_gauge (differences equal in both)
Inverse: h = p/(ρg) | ρ = p/(gh) | ρ = Δp/(gΔh)
Water, g = 10: 10 kPa/m | 10 N/kg | 10 N per litre | kPa × m² = kN
Units: cm ÷ 100 | litres ÷ 1,000 | g/cm³ × 1,000

• Numbers first, with units, before the stem
• Options first — ten times apart means count zeros; 100 kPa apart means gauge versus absolute
• Fluid density for buoyancy; object density for weight
• 'By' is the difference, 'becomes' is the total, 'below' is not 'above'
• Unit and prefix said aloud, then marked — never blank