1Which is the dimensional formula of density?
Density works out to [M L⁻³].
MechanicsClass 11, Mechanical Properties of Fluids
Dimensional formula of Density
[M L-3]
Mass per unit volume. Mass goes up, length goes down by three.
How to get the dimensional formula of density
- Start from the definition: density = mass / volume.
- volume = length3, so volume is [L]3 = [L3].
- Put in the dimension of each part: [M] / [L3].
- Add the powers of each base quantity: [M L-3].
Three questions on density
2What is the SI unit of density?
The SI unit of density is the kilogram per cubic metre (kg/m³).
3Do density and relative density have the same dimensions?
Density is [M L⁻³] but relative density is [M⁰ L⁰ T⁰].
An equation that uses density
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
v = sqrt(Y / ρ)v[L T-1]=sqrt(Y/rho)[L T-1]Dimensionally consistentEvery term is [L T-1]
v = velocityY = Young's modulus
Density: quick answers
What is the dimensional formula of density?
The dimensional formula of density is [M L⁻³]. It comes from density = mass / volume.
What is the SI unit of density?
The SI unit of density is the kilogram per cubic metre (kg/m³).
Is density dimensionless?
No. Density has the dimensions [M L⁻³].