ARCH-P-14: Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P_1V_1 = P_2V_2)

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-14: Why the 145s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~145s (Blows 90s Clock)

Mass of block is

m = \frac{W}{g} = \frac{30}{10} = 3\text{ kg} = 3000\text{ g}

. Net volume of solid material is

V_{\text{net}} = 10^3 - (5^2 \times 10) = 1000 - 250 = 750\text{ cm}^3

. Thus

\rho = \frac{m}{V_{\text{net}}} = \frac{3000}{750} = 4.00\text{ g cm}^{-3}

(~120s).

The Fast ShortcutTarget: 40s (Saves 105s)

Line 1 (Net Material Volume):

V_{\text{net}} = 10(10^2 - 5^2) = 750\text{ cm}^3

; mass

m = 3000\text{ g}

.
Line 2 (Divide):

\rho = \frac{3000}{750} = 4.00\text{ g cm}^{-3}

(25s).

Where Students Lose Time: In 14 past UAT-UK questions (6.01% of Physics), candidates lose 105s by boyle's law p₁*v₁ = p₂*v₂ requires total absolute pressure (atmospheric + piston pressure), never gauge pressure alone. Instead, apply P5 with Maths 1 skill M1.2.

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