Which of the following units is equivalent to one MPa?
1 kN/m2
1 N/cm2
1 kN/mm2
1 N/m2
1 x 106 N/m2
The Correct Answer and Explanation is:
Let’s analyze the question:
Which of the following units is equivalent to one MPa (megapascal)?
Options:
- 1 kN/m²
- 1 N/cm²
- 1 kN/mm²
- 1 N/m²
- 1 × 10⁶ N/m²
Step 1: Understanding the unit MPa
MPa (megapascal) is a unit of pressure or stress in the International System of Units (SI).
- 1 Pa (pascal) = 1 N/m² (one newton per square meter)
- 1 MPa = 1,000,000 Pa = 10⁶ Pa = 10⁶ N/m²
So, 1 MPa = 1,000,000 newtons per square meter.
Step 2: Analyze each option
- 1 kN/m²
- 1 kN = 1,000 N
- So, 1 kN/m² = 1,000 N/m²
- This is not equal to 1,000,000 N/m² (1 MPa), but much smaller.
- 1 N/cm²
- Convert N/cm² to N/m²:
- 1 cm = 0.01 m, so 1 cm² = (0.01 m)² = 0.0001 m²
- Therefore, 1 N/cm² = 1 N per 0.0001 m² = 1 / 0.0001 N/m² = 10,000 N/m²
- This equals 10 kPa, which is not 1 MPa.
- 1 kN/mm²
- 1 kN = 1,000 N
- 1 mm = 0.001 m, so 1 mm² = (0.001)² = 1 × 10⁻⁶ m²
- 1 kN/mm² = 1,000 N per 1 × 10⁻⁶ m² = 1,000 × 10⁶ N/m² = 10⁹ N/m²
- This equals 1 GPa (gigapascal), which is much larger than 1 MPa.
- 1 N/m²
- This is just 1 Pa, very small compared to 1 MPa (which is 1 million Pa).
- 1 × 10⁶ N/m²
- This is exactly 1,000,000 N/m², which equals 1 MPa.
Correct Answer: 1 × 10⁶ N/m²
Explanation (300 words):
The unit megapascal (MPa) is widely used in engineering and physics as a measure of pressure or stress. It represents one million pascals (Pa), and 1 Pa is defined as one newton per square meter (N/m²). The pascal itself measures the force (in newtons) applied uniformly over an area (in square meters). Therefore, to understand which of the given options is equivalent to one MPa, we need to convert each option into the base unit of N/m².
Starting with the simple conversions: 1 kN/m² is 1,000 N/m², which is far smaller than 1,000,000 N/m² (1 MPa). Similarly, 1 N/cm² converts to 10,000 N/m² because one square centimeter is 0.0001 square meters, making this unit smaller than 1 MPa as well. On the other hand, 1 kN/mm² translates into 1,000 N per 1 square millimeter, which is 1,000 N per 1 × 10⁻⁶ m², or 1,000 × 10⁶ N/m², which equals 1 gigapascal (GPa), much larger than 1 MPa.
The unit 1 N/m² equals one pascal, which is much smaller than 1 MPa.
Only 1 × 10⁶ N/m² directly corresponds to 1 MPa because this matches the exact definition of the megapascal — one million pascals.
In summary, understanding unit conversions and the meaning behind the pressure units helps identify that 1 × 10⁶ N/m² is the correct equivalent to one MPa. This knowledge is crucial in fields such as material science, mechanical engineering, and fluid mechanics, where precise pressure and stress measurements are fundamental for safety and performance assessments
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