1Which of these has the same dimensions as kinetic energy?
Kinetic energy and photon energy both have the dimensions [M L² T⁻²].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Kinetic energy
[M L2 T-2]
The energy of motion, 1/2 mv². The factor 1/2 is a pure number and cannot be found by dimensional analysis.
How to get the dimensional formula of kinetic energy
- Start from the definition: kinetic energy = mass × velocity2.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [M] × [L T-1]2.
- Add the powers of each base quantity: [M L2 T-2].
Quantities with the dimensions [M L² T⁻²]
- Work
- 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 kinetic energy with the others in the full grid.
Three questions on kinetic energy
2What is the SI unit of kinetic energy?
The SI unit of kinetic energy is the joule (J).
3Which one has different dimensions from the others?
Displacement is [L]. The other three are all [M L² T⁻²].
An equation that uses kinetic energy
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
K = (1/2) m v2K[M L2 T-2]=1/2 mv2[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
v = velocity
Kinetic energy: quick answers
What is the dimensional formula of kinetic energy?
The dimensional formula of kinetic energy is [M L² T⁻²]. It comes from kinetic energy = mass × velocity².
What is the SI unit of kinetic energy?
The SI unit of kinetic energy is the joule (J).
Which quantities have the same dimensions as kinetic energy?
Kinetic energy shares [M L² T⁻²] with work, energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy, heat. Equal dimensions do not make them the same quantity.