Match the items in List 1 (name of quantities) with those in List 2 (units of quantities in the SI system): M. Dynamic viscosity, N. Kinematic viscosity, O. Surface tension, P. Energy.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 23.03.2021 (Morning Shift)
Detailed Explanation
Fluid mechanics relies on consistent dimensional units in the SI system. Matching physical quantities to their standard units reinforces the fundamental definitions of transport properties and energy.
1. Dynamic viscosity \(\mu = \tau / (du/dy) \rightarrow \text{N}\cdot\text{s/m}^2\) (Item 3)
2. Kinematic viscosity \(\nu = \mu / \rho \rightarrow \text{m}^2/\text{s}\) (Item 4)
3. Surface tension \(\sigma = F / L \rightarrow \text{N/m}\) (Item 1)
4. Energy \(W = F \cdot d \rightarrow \text{N}\cdot\text{m}\) (or Joules) (Item 2)
Why “M-3, N-4, O-1, P-2” Is Correct
Matching M-3, N-4, O-1, and P-2 satisfies all SI definitions, corresponding to option (b).
| Quantity | SI unit | CGS unit | Conversion |
|---|---|---|---|
| Dynamic viscosity μ | Pa·s (N·s/m²) | Poise (P) = dyne·s/cm² | 1 P = 0.1 Pa·s |
| Kinematic viscosity ν = μ/ρ | m²/s | Stoke (St) = cm²/s | 1 St = 10⁻⁴ m²/s |
| Surface tension T | N/m | dyne/cm | 1 dyne/cm = 10⁻³ N/m |
Why the Other Options Are Wrong
- A. M-3, N-4, O-2, P-1: Confuses the units of surface tension (N/m) with energy (N·m).
- C. M-4, N-3, O-1, P-2: Swaps dynamic viscosity (N·s/m²) with kinematic viscosity (m²/s).
- D. M-2, N-4, O-1, P-3: Incorrectly pairs dynamic viscosity with N·m.
Key Point
Dynamic viscosity: N·s/m²; Kinematic viscosity: m²/s; Surface tension: N/m; Energy: N·m.
Key Concepts for Students
- Dynamic viscosity: [M L⁻¹ T⁻¹].
- Kinematic viscosity: [L² T⁻¹].
- Surface tension: [M T⁻²].
- Energy: [M L² T⁻²].
Practice more: this is question 28 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.