1Which of these has the same dimensions as tension?
Tension and centripetal force both have the dimensions [M L T⁻²].
MechanicsClass 11, Laws of Motion
Dimensional formula of Tension
[M L T-2]
The pulling force in a string, rope or rod. It is a force, so it has the dimension of force, and it is not surface tension.
How to get the dimensional formula of tension
- Start from the definition: tension = force.
- 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].
- 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 tension with the others in the full grid.
Three questions on tension
2What is the SI unit of tension?
The SI unit of tension is the newton (N).
3Which one has different dimensions from the others?
Coefficient of restitution is [M⁰ L⁰ T⁰]. The other three are all [M L T⁻²].
An equation that uses tension
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
v = sqrt(T / μ)v[L T-1]=sqrt(T/mu)[L T-1]Dimensionally consistentEvery term is [L T-1]
v = velocity
Tension: quick answers
What is the dimensional formula of tension?
The dimensional formula of tension is [M L T⁻²]. It comes from tension = force.
What is the SI unit of tension?
The SI unit of tension is the newton (N).
Which quantities have the same dimensions as tension?
Tension shares [M L T⁻²] with force, thrust, centripetal force, weight. Equal dimensions do not make them the same quantity.