1Which of these has the same dimensions as spring constant?
Spring constant and surface tension both have the dimensions [M T⁻²].
MechanicsClass 11, Work, Energy and Power
Dimensional formula of Spring constant
[M T-2]
Force per unit stretch. It has the same dimension as surface tension, another trap in exams.
How to get the dimensional formula of spring constant
- Start from the definition: spring constant = force / length.
- 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].
- Put in the dimension of each part: [M L T-2] / [L].
- Add the powers of each base quantity: [M T-2].
Quantities with the dimensions [M T⁻²]
Equal dimensions do not make them the same quantity. Compare spring constant with the others in the full grid.
Three questions on spring constant
2What is the SI unit of spring constant?
The SI unit of spring constant is the newton per metre (N/m).
3Which one has different dimensions from the others?
Tension is [M L T⁻²]. The other three are all [M T⁻²].
Spring constant: quick answers
What is the dimensional formula of spring constant?
The dimensional formula of spring constant is [M T⁻²]. It comes from spring constant = force / length.
What is the SI unit of spring constant?
The SI unit of spring constant is the newton per metre (N/m).
Which quantities have the same dimensions as spring constant?
Spring constant shares [M T⁻²] with surface tension, surface energy. Equal dimensions do not make them the same quantity.