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Playbook

Fluid Mechanics and Properties of Matter

23 q · 30% HARD — the chapter with the highest %HARD in the bank. Buoyancy with density mixing (ρ₁+ρ₂ by equal-volume vs equal-mass), pressure P=hρg, surface tension. Small chapter, dense traps.

questions in the bank
23
tagged HARD
30%
subtopic(s)
2
worked examples
2

When you’ll see it

An Archimedes' buoyancy with floating/sinking, a density-mixing equal-volume/equal-mass, a hydrostatic pressure P = hρg, or a surface-tension statement.

How this chapter is tested

23 q in 10 years · 30% HARD — the chapter with the HIGHEST %HARD in the bank. Two subtopics: Buoyancy / Density / Flotation (16 q · 31% HARD) and Pressure / Surface Tension (7 q · 29% HARD).

Buoyancy F_b = V_submerged · ρ_fluid · g (Archimedes). For floating object: F_b = mg ⟹ V_submerged/V_total = ρ_object/ρ_fluid. The 'sealed packet 1L mass 800g into water (ρ=1), then into liquid B (ρ=1.5)' shape: in water, ρ_packet = 0.8 < 1 ⟹ floats with 80% submerged. In liquid B, ρ_packet = 0.8 < 1.5 ⟹ floats with 0.8/1.5 ≈ 53% submerged.

Density mixing: equal VOLUMES of ρ₁ and ρ₂ ⟹ ρ_avg = (ρ₁+ρ₂)/2 (arithmetic mean). Equal MASSES ⟹ ρ_avg = 2ρ₁ρ₂/(ρ₁+ρ₂) (harmonic mean). Harmonic < arithmetic always (with positive different ρ). The recurring HARD shape: 'mixed in equal volume rel den 4, mixed in equal mass rel den 3, find ρ₁ ρ₂' — set up both equations and solve simultaneously.

The sub-skills

The rules and habits that decide whether you get a question right.

  • Archimedes' principle setup

    F_b = V_submerged × ρ_fluid × g. For floating: F_b = mg ⟹ V_sub/V_total = ρ_object/ρ_fluid. For wholly submerged: V_sub = V_total.

  • Density mixing formulas

    Equal volume: ρ_avg = (ρ₁+ρ₂)/2 (arithmetic mean). Equal mass: ρ_avg = 2ρ₁ρ₂/(ρ₁+ρ₂) (harmonic mean). Harmonic is always smaller.

  • Hydrostatic pressure

    P_gauge = h·ρ·g (depth below free surface). P_absolute = P_atm + h·ρ·g. Pressure same at same depth in connected liquids regardless of container shape.

  • Surface tension qualitative

    Force-per-unit-length along the surface. Causes water-drop sphericity, capillary rise/fall, soap-bubble pressure-jump. Decreases with temperature.

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Fluid Mechanics and Properties of MatterHARD
Two substances of densities ρ1\rho_1 and ρ2\rho_2 are mixed in equal volume and their relative density is 4. When they are mixed in equal masses, relative density is 3. The values of ρ1\rho_1 and ρ2\rho_2 respectively are

[Q65 · Sep · 2019]

Example 2Fluid Mechanics and Properties of MatterHARD
The volume of a sealed packet is 1 litre and its mass is 800 g. The packet is first put inside water with density 1 g cm−3^{-3} and then in another liquid BB with density 1⋅51 \cdot 5 g cm−3^{-3}. Then which one of the following statements holds true?

[Q134 · Sep · 2022]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Equal-volume vs equal-mass arithmetic confusion

    Wrong option swaps the two formulas. Equal volume = arithmetic, equal mass = harmonic. Re-derive from ρ = m_total / V_total in 30 seconds.

  • Using V_total instead of V_submerged for buoyancy

    F_b uses ONLY the volume IN the fluid, not the total volume. For a partially-submerged floating object, V_submerged < V_total. The wrong option uses V_total.

  • Pressure on container walls vs base

    Pressure at the base = hρg, independent of container shape (Pascal). But the FORCE on the walls integrates pressure × area, which DOES depend on shape. Don't conflate pressure with force.

Drill every fluid mechanics and properties of matter question

23 questions from the bank, scoped to 2 bundled subtopics.

Drill the 23 questions

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