Dimensions of Stress: Why It Is the Same as Pressure

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.

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.

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.

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.

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 dimensional formula of stress is [M L^-1 T^-2]. It comes from Force / Area = [M L T^-2] / [L^2].

The SI unit of stress is N/m^2, also called the pascal (Pa). It is the same unit as pressure.

Because both are force per unit area (Force / Area). The same defining formula gives the same dimensions, [M L^-1 T^-2].

Yes. Young's modulus = stress / strain, and strain has no dimensions, so Young's modulus keeps the dimensions of stress: [M L^-1 T^-2].

No. Stress is generally a tensor because it depends on direction, while pressure is a scalar. They only share the same dimensions and unit.