Dimensions & Dimensional Analysis — A/L Physics

How do I practise Dimensions & Dimensional Analysis?

1 question with a worked solution

1. According to Poiseuille's formula and Stokes' law, what are the dimensions of dynamic viscosity (η)?
   1. A) [M L⁻¹ T⁻¹]
   2. B) [M L T⁻²]
   3. C) [M L² T⁻¹]
   4. D) [M L⁻¹ T⁻²]
   Check my answer

   Correct answer: A) [M L⁻¹ T⁻¹]

   From Stokes' Law, viscous force is F = 6πηrv, which gives η = F / (6πrv). Dimensional formula: [η] = [F] / ([r][v]) = [M L T⁻²] / ([L][L T⁻¹]) = [M L⁻¹ T⁻¹].

   Show worked solution

   Step 1: Write Stokes' law: F = 6πηrv. Step 2: Rearrange for η: η = F / (6π r v). Step 3: Insert dimensions: [F] = M L T⁻², [r] = L, [v] = L T⁻¹. Step 4: [η] = [M L T⁻²] / [L² T⁻¹] = M L⁻¹ T⁻¹. Answer: [M L⁻¹ T⁻¹].
   Modelled on: the A/L Physics examination pattern

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Where does Dimensions & Dimensional Analysis fit in the syllabus?

Unit 1.3 · Year 1 · Term 1