Dimensions of Stress: Why It Is the Same as Pressure
Physics · Mechanical Properties Of Solids · NEET
The dimensional formula of stress is [M L^-1 T^-2], and its SI unit is N/m^2 (pascal, Pa). Stress = Force / Area = [M L T^-2] / [L^2] = [M L^-1 T^-2], which is exactly the same as pressure, because both are a force spread over an area. Memory hook: "Stress is just internal pressure" — same formula, same unit, same dimensions.
Both stress and pressure are Force divided by Area, so they share the same dimensional formula [M L^-1 T^-2] and the same SI unit, the pascal (N/m^2).
Your doubts, answered
How do I derive the dimensions of stress step by step?
Stress = Force / Area. Force has dimensions [M L T^-2] (from F = m*a, mass times acceleration). Area has dimensions [L^2]. So Stress = [M L T^-2] / [L^2] = [M L^(1-2) T^-2] = [M L^-1 T^-2]. That is the full dimensional formula of stress.
Why are the dimensions of stress and pressure exactly the same?
Both are defined as a force divided by an area. Pressure = Force / Area and Stress = Force / Area (internal restoring force per unit area). Since the defining formula is identical, the dimensions must be identical: [M L^-1 T^-2]. The physical meaning differs (pressure is external push, stress is the internal reaction), but the units and dimensions match.
What is the SI unit of stress and is it the same as pressure?
Yes. The SI unit of stress is N/m^2, also called the pascal (Pa) — exactly the same as the SI unit of pressure. NCERT states this directly: 1 pascal = 1 N/m^2 for both quantities.
Do Young's modulus and stress have the same dimensions?
Yes. Young's modulus = stress / strain, and strain is dimensionless (it is a ratio of lengths). Dividing by a dimensionless number does not change dimensions, so Young's modulus also has dimensions [M L^-1 T^-2] and unit N/m^2. All moduli of elasticity share this.
If stress equals pressure in dimensions, is stress a scalar too?
Not exactly. Pressure is a scalar with no direction, but stress in general is a tensor (it depends on the direction of the force and the orientation of the surface). They share dimensions but are not the same type of quantity. For NEET numericals you treat stress as Force/Area, giving a magnitude in N/m^2.
⚠️ The NEET trap ✗ Writing dimensions of stress as [M L T^-2] (that is force, not stress). ✓ Stress = Force / Area = [M L T^-2] / [L^2] = [M L^-1 T^-2]. The extra division by area lowers the power of L from +1 to -1. 🧠 Do not confuse the dimensions of stress with the dimensions of force.
Real NEET questions
NEET 2020
Dimensions of stress are:
A · [M L^0 T^-2]
B · [M L^-1 T^-2] ✓
C · [M L T^-2]
D · [M L^2 T^-2]
Solution: Stress = Force / Area. Force = mass * acceleration = [M][L T^-2] = [M L T^-2]. Area = [L^2]. So Stress = [M L T^-2] / [L^2] = [M L^(1-2) T^-2] = [M L^-1 T^-2]. This is the same as the dimensions of pressure. Correct option: B.
Solved Mechanical Properties Of Solids NEET PYQs
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