Pressure in Fluids, Upthrust & Archimedes’ Principle — A/L Physics

How do I practise Pressure in Fluids, Upthrust & Archimedes’ Principle?

1 question with a worked solution

1. A solid metal alloy block weighs 50.0 N in air and 38.0 N when completely immersed in water (density 1000 kg m⁻³). Taking g = 10 m s⁻², what is the volume and density of the metal alloy block?
   1. A) Volume = 2.4 × 10⁻³ m³, Density = 2083 kg m⁻³
   2. B) Volume = 0.6 × 10⁻³ m³, Density = 8333 kg m⁻³
   3. C) Volume = 1.2 × 10⁻³ m³, Density = 4167 kg m⁻³
   4. D) Volume = 1.0 × 10⁻³ m³, Density = 5000 kg m⁻³
   Check my answer

   Correct answer: C) Volume = 1.2 × 10⁻³ m³, Density = 4167 kg m⁻³

   Upthrust U = Weight in air - Apparent weight in water = 50.0 N - 38.0 N = 12.0 N. By Archimedes' Principle: U = V ρ_w g => V = U / (ρ_w g) = 12.0 N / (1000 kg m⁻³ × 10 m s⁻²) = 1.2 × 10⁻³ m³. Mass of block m = W / g = 50.0 N / 10 m s⁻² = 5.0 kg. Density ρ = m / V = 5.0 kg / (1.2 × 10⁻³ m³) ≈ 4166.7 kg m⁻³.

   Show worked solution

   Step 1: Upthrust U = W_air - W_water = 50.0 - 38.0 = 12.0 N. Step 2: Volume V = U / (ρ_w · g) = 12.0 / 10000 = 1.2 × 10⁻³ m³. Step 3: Density ρ = (50.0 / 10) / (1.2 × 10⁻³) = 5.0 / 0.0012 ≈ 4167 kg m⁻³. Answer: Volume = 1.2 × 10⁻³ m³, Density = 4167 kg m⁻³.
   Modelled on: the A/L Physics examination pattern

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Where does Pressure in Fluids, Upthrust & Archimedes’ Principle fit in the syllabus?

Unit 10.5 · Year 2 · Term 3