Viscosity & Fluid Resistance — A/L Physics

How do I practise Viscosity & Fluid Resistance?

1 question with a worked solution

1. A small spherical lead pellet of radius r and density ρ falls vertically under gravity through a viscous liquid of density σ and dynamic viscosity η. When the pellet achieves its constant terminal velocity v_t, which expression gives v_t according to Stokes' Law?
   1. A) v_t = 9 r² (ρ - σ) g / (2 η)
   2. B) v_t = 2 r (ρ - σ) g / (9 η)
   3. C) v_t = 4 r² (ρ - σ) g / (3 η)
   4. D) v_t = 2 r² (ρ - σ) g / (9 η)
   Check my answer

   Correct answer: D) v_t = 2 r² (ρ - σ) g / (9 η)

   At terminal velocity, the net downward force is zero: Weight = Upthrust + Viscous drag => (4/3) π r³ ρ g = (4/3) π r³ σ g + 6πη r v_t => 6πη r v_t = (4/3) π r³ (ρ - σ) g => v_t = 2 r² (ρ - σ) g / (9 η).

   Show worked solution

   Step 1: Balance forces: W = U + F_viscous. Step 2: 4/3 π r³ ρ g = 4/3 π r³ σ g + 6π η r v_t. Step 3: 6π η r v_t = 4/3 π r³ (ρ - σ) g => v_t = 2 r² (ρ - σ) g / (9 η). Answer: v_t = 2 r² (ρ - σ) g / (9 η).
   Modelled on: the A/L Physics examination pattern

Get this auto-marked

Next in the syllabus

Where does Viscosity & Fluid Resistance fit in the syllabus?

Unit 10.3 · Year 2 · Term 3