If 850 kg liquid occupies volume of one cubic meter, then 0.85 represents its:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 4 MARCH 2017 Morning Shift
Detailed Explanation
Specific gravity expresses the density of a substance relative to pure water. Comparing the given mass density to standard water density determines this ratio.
Given: mass \(m = 850\text{ kg}\), volume \(V = 1\text{ m}^3\):
\[ \rho = \frac{m}{V} = \frac{850\text{ kg}}{1\text{ m}^3} = 850\text{ kg/m}^3 \]
Comparing with the density of water (\(\rho_{\text{water}} = 1000\text{ kg/m}^3\)):
\[ S = \frac{\rho}{\rho_{\text{water}}} = \frac{850}{1000} = 0.85 \]
Why “Specific gravity” Is Correct
Dividing the liquid density (850 kg/m³) by 1000 kg/m³ gives 0.85, which is the definition of specific gravity.
| 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. Specific weight: Specific weight is ρg = 850 × 9.81 = 8338.5 N/m³, not 0.85.
- B. Specific mass: Specific mass is synonymous with mass density (850 kg/m³).
- D. Specific density: Specific density is an informal term for mass density or specific gravity, but the standard engineering term is specific gravity.
Key Point
Specific gravity S = ρ / 1000 kg/m³; 850 / 1000 = 0.85.
Key Concepts for Students
- Specific gravity is dimensionless.
- Fluids with S < 1.0 (such as 0.85) float on water.
- Specific gravity is determined experimentally using hydrometers or pycnometers.
Practice more: this is question 58 in Properties of Fluid MCQs – Part 4. Try the whole set and check every answer instantly.