The SI unit of stress is same as the SI unit of

• A. Strain
• B. Modulus of elasticity
• C. Pressure
• D. Both (2) and (3)

The SI unit of stress is indeed the same as the SI unit of both pressure and the modulus of elasticity. To clarify this, let’s break down what stress is and how it relates to these other concepts.

Understanding Stress

Stress is defined as the force applied per unit area within materials. It is a measure of the internal resistance of a material to deformation when subjected to an external load. The formula for stress (σ) is given by:

σ = F / A

Where:

• σ = stress (in pascals, Pa)
• F = force applied (in newtons, N)
• A = area over which the force is applied (in square meters, m²)

SI Units Explained

The SI unit of force is the newton (N), and the SI unit of area is square meters (m²). Therefore, when we calculate stress, we have:

1 Pascal (Pa) = 1 N/m²

This means that stress is measured in pascals, which is also the unit for pressure. Pressure is defined similarly, as it is also the force applied per unit area.

Relationship with Modulus of Elasticity

The modulus of elasticity, or Young's modulus, is a measure of a material's ability to deform elastically (i.e., non-permanently) when a force is applied. It is defined as the ratio of stress to strain:

E = σ / ε

Where:

• E = modulus of elasticity (in pascals, Pa)
• ε = strain (dimensionless)

Since the modulus of elasticity is expressed in terms of stress (which is in pascals), it also shares the same unit of measurement.

Conclusion on the Options

Now, looking at the options provided:

• A. Strain - This is dimensionless and does not have a unit.
• B. Modulus of elasticity - This is measured in pascals (Pa).
• C. Pressure - This is also measured in pascals (Pa).
• D. Both (2) and (3) - This is correct since both modulus of elasticity and pressure share the same unit as stress.

Thus, the correct answer is D. Both (2) and (3). Stress, pressure, and the modulus of elasticity are all measured in pascals, highlighting the interconnectedness of these concepts in material science and engineering.