Calculate the approximate mass density of oil with 4.5 m³ of volume and 40 kN of weight (Consider g = 10 m/s²).
Try it first: pick an option, then read the explanation.
Asked in SSC JE 10/10/2023 (05pm-07pm)
Detailed Explanation
Mass density is the mass per unit volume of a substance. The mass is obtained from weight using Newton's second law (W = mg), and then divided by the total volume.
Given weight \(W = 40\text{ kN} = 40{,}000\text{ N}\), volume \(V = 4.5\text{ m}^3\), and \(g = 10\text{ m/s}^2\):
\[ m = \frac{W}{g} = \frac{40{,}000\text{ N}}{10\text{ m/s}^2} = 4000\text{ kg} \]
\[ \rho = \frac{m}{V} = \frac{4000\text{ kg}}{4.5\text{ m}^3} = 888.89\text{ kg/m}^3 \approx 889\text{ kg/m}^3 \]
Why “889 kg/m³” Is Correct
Dividing 4000 kg by 4.5 m³ gives 888.89 kg/m³, which rounds to 889 kg/m³.
| 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
- B. 809 kg/m³: 809 kg/m³ results from an arithmetic error in the division.
- C. 920 kg/m³: 920 kg/m³ would correspond to a heavier oil of approximately 41.4 kN.
- D. 850 kg/m³: 850 kg/m³ is a typical nominal oil density but does not match the given numbers.
Key Point
Mass density ρ = m / V = W / (gV); 40,000 / (10 × 4.5) ≈ 889 kg/m³.
Key Concepts for Students
- Mass density ρ has SI units of kg/m³ and dimensions [M L⁻³].
- Specific gravity S = ρ / ρ_water = 889 / 1000 = 0.889.
- Density is an intensive state property that varies with temperature and pressure.
Practice more: this is question 11 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.