1Which of these has the same dimensions as work?
Work and strain energy both have the dimensions [M L² T⁻²].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Work
[M L2 T-2]
Force times displacement along the force. Work, energy and torque share one dimension but are different quantities.
How to get the dimensional formula of work
- Start from the definition: work = force × displacement.
- 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].
- displacement = length, so displacement is [L] = [L].
- Put in the dimension of each part: [M L T-2] × [L].
- Add the powers of each base quantity: [M L2 T-2].
Quantities with the dimensions [M L² T⁻²]
- Energy
- Kinetic energy
- Potential energy
- Torque
- Torsional constant
- Gravitational potential energy
- Strain energy
- Heat
- Internal energy
- Electric potential energy
- Work function
- Photon energy
- Binding energy
Equal dimensions do not make them the same quantity. Compare work with the others in the full grid.
Three questions on work
2What is the SI unit of work?
The SI unit of work is the joule (J).
3Which one has different dimensions from the others?
Angular velocity is [T⁻¹]. The other three are all [M L² T⁻²].
An equation that uses work
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
W = F s cos(θ)W[M L2 T-2]=F s cos(theta)[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
θ = angle
Work: quick answers
What is the dimensional formula of work?
The dimensional formula of work is [M L² T⁻²]. It comes from work = force × displacement.
What is the SI unit of work?
The SI unit of work is the joule (J).
Which quantities have the same dimensions as work?
Work shares [M L² T⁻²] with energy, kinetic energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy, heat. Equal dimensions do not make them the same quantity.