1Which of these has the same dimensions as coefficient of restitution?
Coefficient of restitution and relative permeability both have the dimensions [M⁰ L⁰ T⁰].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Coefficient of restitution
[M0 L0 T0]
The ratio of speed of separation to speed of approach in a collision. It is a pure number between 0 and 1.
How to get the dimensional formula of coefficient of restitution
- Start from the definition: coefficient of restitution = velocity / velocity.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [L T-1] / [L T-1].
- Add the powers of each base quantity: [M0 L0 T0].
Quantities with the dimensions [M⁰ L⁰ T⁰]
- Angle
- Solid angle
- Coefficient of friction
- Relative density
- Strain
- 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 coefficient of restitution with the others in the full grid.
Three questions on coefficient of restitution
2Which of these has no dimensions at all?
Coefficient of restitution is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Centripetal force is [M L T⁻²]. The other three are all [M⁰ L⁰ T⁰].
Coefficient of restitution: quick answers
What is the dimensional formula of coefficient of restitution?
The dimensional formula of coefficient of restitution is [M⁰ L⁰ T⁰]. It comes from coefficient of restitution = velocity / velocity.
What is the SI unit of coefficient of restitution?
Coefficient of restitution has no unit, because it is a pure number.
Is coefficient of restitution dimensionless?
Yes. Coefficient of restitution is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].