1Which of these has the same dimensions as centripetal force?
Centripetal force and weight both have the dimensions [M L T⁻²].
MechanicsClass 11, Motion in a Plane
Dimensional formula of Centripetal force
[M L T-2]
The inward force mv²/r that keeps a body on a circle. It is a force, so it has the dimension of force.
How to get the dimensional formula of centripetal force
- Start from the definition: centripetal force = mass × velocity2 / length.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [M] × [L T-1]2 / [L].
- 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 centripetal force with the others in the full grid.
Three questions on centripetal force
2What is the SI unit of centripetal force?
The SI unit of centripetal force is the newton (N).
3Which one has different dimensions from the others?
Volume is [L³]. The other three are all [M L T⁻²].
Centripetal force: quick answers
What is the dimensional formula of centripetal force?
The dimensional formula of centripetal force is [M L T⁻²]. It comes from centripetal force = mass × velocity² / length.
What is the SI unit of centripetal force?
The SI unit of centripetal force is the newton (N).
Which quantities have the same dimensions as centripetal force?
Centripetal force shares [M L T⁻²] with force, tension, thrust, weight. Equal dimensions do not make them the same quantity.