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