Density of a fluid is its mass per unit volume. The dimension of density of a fluid is:
Try it first: pick an option, then read the explanation.
Correct answer: C. M L⁻³
Asked in SSC JE 14.11.2022
Detailed Explanation
Mass density (ρ) measures the compactness of matter within a given space. Dimensional analysis expresses this fundamental property in terms of base dimensions mass [M] and length [L].
\[ \rho = \frac{\text{Mass}}{\text{Volume}} = \frac{[M]}{[L^3]} = [M L^{-3}] \]
Why “M L⁻³” Is Correct
Mass has dimension \([M]\) and volume has dimension \([L^3]\). Dividing mass by volume yields \([M L^{-3}]\).
| Property | Formula | SI unit | Standard value (water, 4°C) |
|---|---|---|---|
| Density ρ | m/V | kg/m³ | 1000 kg/m³ |
| Specific weight γ | ρg | N/m³ | 9810 N/m³ |
| Specific gravity S | ρ/ρ_water | — | 1.0 |
| Specific volume v | 1/ρ | m³/kg | 0.001 m³/kg |
| Bulk modulus K | −dp/(dV/V) | Pa | 2.06 GPa |
| Compressibility β | 1/K | Pa⁻¹ | 4.85 × 10⁻¹⁰ Pa⁻¹ |
Why the Other Options Are Wrong
- A. M L T⁻²: M L T⁻² is the dimension of force, not density.
- B. kg/m³: kg/m³ is the physical unit in the SI system, whereas the question asks for the dimensional formula.
- D. M³ L⁻³: M³ L⁻³ is dimensionally incorrect.
Key Point
Dimension of mass density ρ = [M L⁻³].
Key Concepts for Students
- Mass density has SI units of kg/m³ and CGS units of g/cm³.
- Dimensional formula relates fundamental physical quantities M, L, T.
- Specific weight γ = ρg has dimensions [M L⁻² T⁻²].
Practice more: this is question 23 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.