1Which of these has the same dimensions as displacement?
Displacement and Bohr radius both have the dimensions [L].
MechanicsClass 11, Motion in a Straight Line
Dimensional formula of Displacement
[L]
The change in position, measured from start to end. It has the dimension of length even though it also has a direction.
How to get the dimensional formula of displacement
- Start from the definition: displacement = length.
- Put in the dimension of each part: [L].
- Add the powers of each base quantity: [L].
Quantities with the dimensions [L]
- Length
- Radius of gyration
- Mean free path
- Wavelength
- Amplitude
- Focal length
- Fringe width
- de Broglie wavelength
- Bohr radius
Equal dimensions do not make them the same quantity. Compare displacement with the others in the full grid.
Three questions on displacement
2What is the SI unit of displacement?
The SI unit of displacement is the metre (m).
3Which one has different dimensions from the others?
Velocity is [L T⁻¹]. The other three are all [L].
An equation that uses displacement
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
s = u t + (1/2) a t2s[L]=ut[L]+1/2 at2[L]Dimensionally consistentEvery term is [L]
t = timea = acceleration
Displacement: quick answers
What is the dimensional formula of displacement?
The dimensional formula of displacement is [L]. It comes from displacement = length.
What is the SI unit of displacement?
The SI unit of displacement is the metre (m).
Which quantities have the same dimensions as displacement?
Displacement shares [L] with length, radius of gyration, mean free path, wavelength, amplitude, focal length, fringe width, de Broglie wavelength. Equal dimensions do not make them the same quantity.