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UAT-UK SPEC: P5MODULE: PHYSICSTOPIC ID: ARCH-P-14

Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P(1V, 1) = P(2V, 2))

Master Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P(1V, 1) = P(2V, 2)) on the ESAT Physics paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 40s, saving +105s per question.

Standard Classroom Time
145s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
40s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+105s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Net Material Volume): Vnet=10(102−52)=750 cm3V_{\text{net}} = 10(10^2 - 5^2) = 750\text{ cm}^3; mass m=3000 gm = 3000\text{ g}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Divide): ρ=3000750=4.00 g cm−3\rho = \frac{3000}{750} = 4.00\text{ g cm}^{-3} (25s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1subsystem_isolation_trap

Using piston additional pressure ΔP = mg/A alone instead of total absolute trapped gas pressure P₂ = P(atm) + mg/A in Boyle's Law

Boyle's Law P₁*V₁ = P₂*V₂ requires total absolute pressure (atmospheric + piston pressure), never gauge pressure alone.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2sign_or_direction_flip

Dividing density by 1.20 instead of multiplying by 1.20 when isothermal gas pressure increases by 20%

For fixed mass m at constant T, P*V = const and ρ = m/V, so density ρ is directly proportional to pressure P (ρ₂ = 1.20 * ρ₁).

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3fence_post_or_domain_trap

Using Celsius T(°C) instead of Kelvin T(K) = T(°C) + 273 in ideal gas scaling P*V/T = const

Ideal gas law requires absolute temperature in Kelvin.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P(1V, 1) = P(2V, 2))

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Full Lesson All 15 Questions (ARCH-P-14)
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ARCH-P-14: Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P(1V, 1) = P(2V, 2)) (Sample)Physics
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SUB-90 ZONE (<40S)
0.0s40s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-P-14 (6-Card Lesson)Format: Standard 5-Option
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Question 1 of 1 • 90s Target

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