1Which of these has the same dimensions as force?
Force and tension both have the dimensions [M L T⁻²].
MechanicsClass 11, Laws of Motion
Dimensional formula of Force
[M L T-2]
Mass times acceleration, from Newton's second law. One newton is one kg m/s².
How to get the dimensional formula of force
- Start from the definition: force = mass × acceleration.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- Put in the dimension of each part: [M] × [L T-2].
- Add the powers of each base quantity: [M L T-2].
Quantities with the dimensions [M L T⁻²]
Equal dimensions do not make them the same quantity. Compare force with the others in the full grid.
Three questions on force
2What is the SI unit of force?
The SI unit of force is the newton (N).
3Which one has different dimensions from the others?
Jerk is [L T⁻³]. The other three are all [M L T⁻²].
An equation that uses force
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
F = G m1 m2 / r2F[M L T-2]=G m1 m2 / r2[M L T-2]Dimensionally consistentEvery term is [M L T-2]
r = length
Force: quick answers
What is the dimensional formula of force?
The dimensional formula of force is [M L T⁻²]. It comes from force = mass × acceleration.
What is the SI unit of force?
The SI unit of force is the newton (N).
Which quantities have the same dimensions as force?
Force shares [M L T⁻²] with tension, thrust, centripetal force, weight. Equal dimensions do not make them the same quantity.