The reciprocal of density is known as specific volume. The dimension of specific volume of a fluid is:
Try it first: pick an option, then read the explanation.
Correct answer: C. M⁻¹ L³
Asked in SSC JE 14.11.2022
Detailed Explanation
Specific volume represents the space occupied by a unit mass of material. As the reciprocal of mass density, its dimensions are inverted relative to density.
From the definition of specific volume \(v\):
\[ v = \frac{1}{\rho} = \frac{\text{Volume}}{\text{Mass}} = \frac{[L^3]}{[M]} = [M^{-1} L^3] \]
Why “M⁻¹ L³” Is Correct
Because volume has dimensions \([L^3]\) and mass has dimensions \([M]\), specific volume has dimensions \([M^{-1} L^3]\).
| 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. M⁰ L³: M⁰ L³ represents total volume [L³], omitting the per-unit-mass dimension.
- B. m³/kg: m³/kg is the SI unit of specific volume, not its dimensional formula.
- D. M L T⁻²: M L T⁻² represents force (Newtons), not specific volume.
Key Point
Dimension of specific volume v = 1/ρ is [M⁻¹ L³].
Key Concepts for Students
- Specific volume has SI units of m³/kg.
- In thermodynamics, specific volume is an intensive property.
- For an incompressible fluid like liquid water, v ≈ 0.001 m³/kg.
Practice more: this is question 22 in Properties of Fluid MCQs – Part 2. Try the whole set and check every answer instantly.