Question

Units for stress are

• A. MPa
• B. Pa/m\(^2\)
• C. Kg/m
• D. No units

Hint:

Remember the fundamental definition: Stress = Force / Area. This will always lead you to the correct units (N/m\(^2\) or Pa). Engineering stress values are often large, so prefixes like Mega (M) for \(10^6\) and Giga (G) for \(10^9\) are very common.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Stress (\(\sigma\)) is a fundamental concept in mechanics and materials science. It is defined as the internal force per unit area that particles of a continuous material exert on each other.

Step 2: Key Formula or Approach:
The formula for engineering stress is: \[ \sigma = \frac{F}{A_0} \] where \(F\) is the applied force and \(A_0\) is the original cross-sectional area.

Step 3: Detailed Explanation:
Let's derive the units:

• The SI unit for force (\(F\)) is the Newton (N).

• The SI unit for area (\(A_0\)) is the square meter (m\(^2\)).

• Therefore, the SI unit for stress is N/m\(^2\).

• One Newton per square meter is defined as one Pascal (Pa). So, \(1 \text{ Pa} = 1 \text{ N/m}^2\).
Now let's analyze the options:

• (A) MPa: This stands for MegaPascal. Mega is the SI prefix for \(10^6\). So, \(1 \text{ MPa} = 10^6 \text{ Pa}\). Since Pa is the unit of stress, MPa is also a valid and very commonly used unit for stress in engineering applications, as the stresses in materials are often in the millions of Pascals.

• (B) Pa/m\(^2\): This would be (N/m\(^2\))/m\(^2\) = N/m\(^4\), which is incorrect.

• (C) Kg/m: This is a unit of linear density (mass per unit length), which is incorrect.

• (D) No units: Stress is a physical quantity and has units. This is incorrect.

Step 4: Final Answer:
MPa (MegaPascal) is a standard and correct unit for stress.