1Which is the dimensional formula of linear mass density?
Linear mass density works out to [M L⁻¹].
Oscillations and wavesClass 11, Waves
Dimensional formula of Linear mass density
[M L-1]
Mass per unit length of a string. It appears in the speed of a wave on a string, sqrt(T/μ).
How to get the dimensional formula of linear mass density
- Start from the definition: linear mass density = mass / length.
- Put in the dimension of each part: [M] / [L].
- Add the powers of each base quantity: [M L-1].
Three questions on linear mass density
2What is the SI unit of linear mass density?
The SI unit of linear mass density is the kilogram per metre (kg/m).
3Do linear mass density and intensity of a wave have the same dimensions?
Linear mass density is [M L⁻¹] but intensity of a wave is [M T⁻³].
An equation that uses linear mass 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(T / μ)v[L T-1]=sqrt(T/mu)[L T-1]Dimensionally consistentEvery term is [L T-1]
v = velocity
Linear mass density: quick answers
What is the dimensional formula of linear mass density?
The dimensional formula of linear mass density is [M L⁻¹]. It comes from linear mass density = mass / length.
What is the SI unit of linear mass density?
The SI unit of linear mass density is the kilogram per metre (kg/m).
Is linear mass density dimensionless?
No. Linear mass density has the dimensions [M L⁻¹].