1Which of these has the same dimensions as strain?
Strain and emissivity both have the dimensions [M⁰ L⁰ T⁰].
Properties of matterClass 11, Mechanical Properties of Solids
Dimensional formula of Strain
[M0 L0 T0]
Change in length divided by the original length, so it is a pure number.
How to get the dimensional formula of strain
- Start from the definition: strain = length / length.
- Put in the dimension of each part: [L] / [L].
- Add the powers of each base quantity: [M0 L0 T0].
Quantities with the dimensions [M⁰ L⁰ T⁰]
- Angle
- Solid angle
- Coefficient of friction
- Coefficient of restitution
- Relative density
- Poisson's ratio
- Reynolds number
- Emissivity
- Ratio of specific heats
- Sound level
- Relative permittivity
- Magnetic susceptibility
- Relative permeability
- Power factor
- Quality factor
- Refractive index
- Magnification
Equal dimensions do not make them the same quantity. Compare strain with the others in the full grid.
Three questions on strain
2Which of these has no dimensions at all?
Strain is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Velocity gradient is [T⁻¹]. The other three are all [M⁰ L⁰ T⁰].
Strain: quick answers
What is the dimensional formula of strain?
The dimensional formula of strain is [M⁰ L⁰ T⁰]. It comes from strain = length / length.
What is the SI unit of strain?
Strain has no unit, because it is a pure number.
Is strain dimensionless?
Yes. Strain is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].