If the specific weight of a certain liquid is 5000 N/m³, then calculate the specific volume (in m³/N).
Try it first: pick an option, then read the explanation.
Correct answer: D. 0.0002
Asked in SSC JE 06/06/2024 (09am-11am)
Detailed Explanation
Specific weight is the weight per unit volume (N/m³). When specific volume is expressed in units of m³/N, it represents the volume occupied per unit weight of fluid, which is the exact reciprocal of specific weight.
Given specific weight \(\gamma = 5000\text{ N/m}^3\):
\[ v = \frac{1}{\gamma} = \frac{1}{5000\text{ N/m}^3} = 0.0002\text{ m}^3/\text{N} \]
Why “0.0002” Is Correct
Dividing 1 by 5000 N/m³ gives 0.0002 m³/N, matching option (d).
| 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. 0.002: 0.002 corresponds to 1/500, an error by a factor of 10.
- B. 0.2: 0.2 corresponds to 1/5.
- C. 0.02: 0.02 corresponds to 1/50.
Key Point
Specific volume (m³/N) = 1 / specific weight (N/m³); 1 / 5000 = 0.0002 m³/N.
Key Concepts for Students
- In standard SI, specific volume is defined per unit mass (m³/kg = 1/ρ).
- When specified in exam questions as m³/N, specific volume equals 1/γ.
- Specific weight γ = ρg (9810 N/m³ for water at 4°C).
Practice more: this is question 6 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.