1Which of these has the same dimensions as stress?
Stress and Young's modulus both have the dimensions [M L⁻¹ T⁻²].
Properties of matterClass 11, Mechanical Properties of Solids
Dimensional formula of Stress
[M L-1 T-2]
Restoring force per unit area inside a body. It has the same dimension as pressure and the elastic moduli.
How to get the dimensional formula of stress
- Start from the definition: stress = force / area.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- area = length × length, so area is [L] × [L] = [L2].
- Put in the dimension of each part: [M L T-2] / [L2].
- Add the powers of each base quantity: [M L-1 T-2].
Quantities with the dimensions [M L⁻¹ T⁻²]
Equal dimensions do not make them the same quantity. Compare stress with the others in the full grid.
Three questions on stress
2What is the SI unit of stress?
The SI unit of stress is the pascal (Pa).
3Which one has different dimensions from the others?
Surface energy is [M T⁻²]. The other three are all [M L⁻¹ T⁻²].
Stress: quick answers
What is the dimensional formula of stress?
The dimensional formula of stress is [M L⁻¹ T⁻²]. It comes from stress = force / area.
What is the SI unit of stress?
The SI unit of stress is the pascal (Pa).
Which quantities have the same dimensions as stress?
Stress shares [M L⁻¹ T⁻²] with energy density, pressure, strain energy density, Young's modulus, bulk modulus, shear modulus. Equal dimensions do not make them the same quantity.