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Oil in a hydraulic cylinder is compressed from an initial volume 2 m3 to 1.96 m3. If the pressure of oil in the cylinder changes from 40 MPa to 80 MPa during compression, the bulk modulus of elasticity of oil is _____
  • a)
    1000 MPa
  • b)
    2000 MPa
  • c)
    4000 MPa
  • d)
    8000 MPa
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Oil in a hydraulic cylinder is compressed from an initial volume 2 m3 ...
Bulk modulus of elasticity of oil
Hence, the correct option is (b).
Free Test
Community Answer
Oil in a hydraulic cylinder is compressed from an initial volume 2 m3 ...
Understanding Bulk Modulus of Elasticity
The bulk modulus of elasticity (K) is a measure of a material's resistance to uniform compression. It is defined by the formula:
K = -ΔP / (ΔV/V₀)
Where:
- ΔP = Change in pressure
- ΔV = Change in volume
- V₀ = Initial volume
Given Data
- Initial volume (V₀) = 2 m³
- Final volume (V) = 1.96 m³
- Initial pressure (P₀) = 40 MPa
- Final pressure (P) = 80 MPa
Calculating the Change in Pressure
- ΔP = P - P₀ = 80 MPa - 40 MPa = 40 MPa
Calculating the Change in Volume
- ΔV = V - V₀ = 1.96 m³ - 2 m³ = -0.04 m³ (a decrease in volume)
Calculating the Initial Volume Ratio
- V₀ = 2 m³
Plugging Values into the Bulk Modulus Formula
Now we can calculate the bulk modulus:
K = -ΔP / (ΔV/V₀)
K = -40 MPa / (-0.04 m³ / 2 m³)
K = -40 MPa / (-0.02)
K = 2000 MPa
Conclusion
The calculated bulk modulus of elasticity of the oil is 2000 MPa, which confirms that the correct answer is option 'B'.
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Oil in a hydraulic cylinder is compressed from an initial volume 2 m3 to 1.96 m3. If the pressure of oil in the cylinder changes from 40 MPa to 80 MPa during compression, the bulk modulus of elasticity of oil is _____a)1000 MPab)2000 MPac)4000 MPad)8000 MPaCorrect answer is option 'B'. Can you explain this answer?
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