In mechanics of solids, stress is defined as the internal force acting per unit area within a material. In SI units, stress is measured in which of the following units?

Introduction / Context:

Stress is a fundamental concept in the study of strength of materials and solid mechanics. It quantifies how internal forces are distributed over a cross sectional area inside a material when external loads are applied. Knowing the correct SI unit for stress is essential for solving numerical problems and interpreting material properties like yield strength and ultimate strength. This question asks you to identify the proper SI unit of stress from a list of different physical units.

Given Data / Assumptions:

• Stress σ is defined as force per unit area: σ = F / A.
• Force F in SI is measured in newtons (N).
• Area A in SI is measured in square metres (m^2).
• Pressure is also defined as force per unit area and uses the same unit.

Concept / Approach:

Since stress is force per unit area, its SI unit must be the same as that of pressure. In SI, one pascal (Pa) is defined as one newton per square metre: 1 Pa = 1 N m^-2. Thus, the unit of stress is pascal. The other options represent completely different physical quantities: newton second for impulse or momentum units, steradian for solid angle, joule for energy and watt for power. None of these match the dimensional formula of stress, which is M L^-1 T^-2 in terms of mass, length and time.

Step-by-Step Solution:

Verification / Alternative check:

Material property tables list yield stress, ultimate tensile stress and compressive stress in units of MPa (megapascal) or sometimes N mm^-2, which is numerically equivalent to MPa. For example, a structural steel might have a yield stress of 250 MPa. Since MPa stands for 10^6 pascal, this confirms that pascal is the base unit for stress. The fact that pressure and stress share the same unit reflects that both are force per unit area, though stress is usually internal and can be tensile or compressive, while pressure is usually external and compressive.

Why Other Options Are Wrong:

Option A (newton second): This unit is associated with impulse or momentum (since momentum has units kg m s^-1 and newton second is equivalent to that), not with stress.

Option B (steradian): This is the SI unit of solid angle in three dimensional geometry.

Option D (joule): This is the SI unit of energy or work, equal to N m, not N m^-2.

Option E (watt): This is the SI unit of power, equal to joule per second (J s^-1).

Common Pitfalls:

Students sometimes confuse stress with strain or pressure. Strain is dimensionless, being a ratio of change in length to original length, so it has no unit. Pressure has the same unit as stress but applies to fluids or external forces on surfaces. Remember that any time you see force divided by area in a mechanical context, the result is measured in pascals. For engineering materials, you usually work with kilopascal (kPa), megapascal (MPa) or gigapascal (GPa) due to the large magnitudes involved.

Final Answer:

The SI unit of stress is the pascal (Pa).