1Which of these has the same dimensions as root mean square velocity?
Root mean square velocity and speed of light both have the dimensions [L T⁻¹].
Heat and thermodynamicsClass 11, Kinetic Theory
Dimensional formula of Root mean square velocity
[L T-1]
The square root of the mean of the squares of the molecular speeds, √(3RT/M). It has the dimension of velocity.
How to get the dimensional formula of root mean square velocity
- Start from the definition: root mean square velocity = velocity.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [L T-1].
- Add the powers of each base quantity: [L T-1].
Quantities with the dimensions [L T⁻¹]
Equal dimensions do not make them the same quantity. Compare root mean square velocity with the others in the full grid.
Three questions on root mean square velocity
2What is the SI unit of root mean square velocity?
The SI unit of root mean square velocity is the metre per second (m/s).
3Which one has different dimensions from the others?
Internal energy is [M L² T⁻²]. The other three are all [L T⁻¹].
Root mean square velocity: quick answers
What is the dimensional formula of root mean square velocity?
The dimensional formula of root mean square velocity is [L T⁻¹]. It comes from root mean square velocity = velocity.
What is the SI unit of root mean square velocity?
The SI unit of root mean square velocity is the metre per second (m/s).
Which quantities have the same dimensions as root mean square velocity?
Root mean square velocity shares [L T⁻¹] with velocity, escape velocity, speed of light. Equal dimensions do not make them the same quantity.