1Which of these has the same dimensions as energy density?
Energy density and shear modulus both have the dimensions [M L⁻¹ T⁻²].
MechanicsClass 12, Electromagnetic Induction
Dimensional formula of Energy density
[M L-1 T-2]
Energy stored per unit volume. It has the same dimension as pressure, as in the energy of an electric field.
How to get the dimensional formula of energy density
- Start from the definition: energy density = energy / volume.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- volume = length3, so volume is [L]3 = [L3].
- Put in the dimension of each part: [M L2 T-2] / [L3].
- Add the powers of each base quantity: [M L-1 T-2].
Quantities with the dimensions [M L⁻¹ T⁻²]
Equal dimensions do not make them the same quantity. Compare energy density with the others in the full grid.
Three questions on energy density
2What is the SI unit of energy density?
The SI unit of energy density is the joule per cubic metre (J/m³).
3Which one has different dimensions from the others?
Coefficient of restitution is [M⁰ L⁰ T⁰]. The other three are all [M L⁻¹ T⁻²].
Energy density: quick answers
What is the dimensional formula of energy density?
The dimensional formula of energy density is [M L⁻¹ T⁻²]. It comes from energy density = energy / volume.
What is the SI unit of energy density?
The SI unit of energy density is the joule per cubic metre (J/m³).
Which quantities have the same dimensions as energy density?
Energy density shares [M L⁻¹ T⁻²] with pressure, stress, strain energy density, Young's modulus, bulk modulus, shear modulus. Equal dimensions do not make them the same quantity.