1Which of these has the same dimensions as Poisson's ratio?
Poisson's ratio and refractive index both have the dimensions [M⁰ L⁰ T⁰].
Properties of matterClass 11, Mechanical Properties of Solids
Dimensional formula of Poisson's ratio
[M0 L0 T0]
Lateral strain divided by longitudinal strain. Both are pure numbers, so this is too.
How to get the dimensional formula of Poisson's ratio
- Start from the definition: Poisson's ratio = strain / strain.
- strain = length / length, so strain is [L] / [L] = [M0 L0 T0].
- Put in the dimension of each part: [M0 L0 T0] / [M0 L0 T0].
- 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
- Strain
- 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 Poisson's ratio with the others in the full grid.
Three questions on Poisson's ratio
2Which of these has no dimensions at all?
Poisson's ratio is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Strain energy is [M L² T⁻²]. The other three are all [M⁰ L⁰ T⁰].
Poisson's ratio: quick answers
What is the dimensional formula of Poisson's ratio?
The dimensional formula of Poisson's ratio is [M⁰ L⁰ T⁰]. It comes from Poisson's ratio = strain / strain.
What is the SI unit of Poisson's ratio?
Poisson's ratio has no unit, because it is a pure number.
Is Poisson's ratio dimensionless?
Yes. Poisson's ratio is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].