1Which of these has the same dimensions as weight?
Weight and force both have the dimensions [M L T⁻²].
MechanicsClass 11, Laws of Motion
Dimensional formula of Weight
[M L T-2]
The force of gravity on a body, mass times g. Weight is a force, so unlike mass it has a time in its dimension.
How to get the dimensional formula of weight
- Start from the definition: weight = mass × acceleration due to gravity.
- 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].
- gravitational constant = force × length2 / mass2, so gravitational constant is [M L T-2] × [L]2 / [M]2 = [M-1 L3 T-2].
- acceleration due to gravity = gravitational constant × mass / length2, so acceleration due to gravity is [M-1 L3 T-2] × [M] / [L]2 = [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 weight with the others in the full grid.
Three questions on weight
2What is the SI unit of weight?
The SI unit of weight is the newton (N).
3Which one has different dimensions from the others?
Potential energy is [M L² T⁻²]. The other three are all [M L T⁻²].
Weight: quick answers
What is the dimensional formula of weight?
The dimensional formula of weight is [M L T⁻²]. It comes from weight = mass × acceleration due to gravity.
What is the SI unit of weight?
The SI unit of weight is the newton (N).
Which quantities have the same dimensions as weight?
Weight shares [M L T⁻²] with force, tension, thrust, centripetal force. Equal dimensions do not make them the same quantity.