1Which of these has the same dimensions as gravitational field intensity?
Gravitational field intensity and acceleration due to gravity both have the dimensions [L T⁻²].
GravitationClass 11, Gravitation
Dimensional formula of Gravitational field intensity
[L T-2]
The gravitational force on a unit mass. It has the dimension of acceleration, and near the Earth it is g.
How to get the dimensional formula of gravitational field intensity
- Start from the definition: gravitational field intensity = force / mass.
- 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] / [M].
- Add the powers of each base quantity: [L T-2].
Quantities with the dimensions [L T⁻²]
Equal dimensions do not make them the same quantity. Compare gravitational field intensity with the others in the full grid.
Three questions on gravitational field intensity
2What is the SI unit of gravitational field intensity?
The SI unit of gravitational field intensity is the newton per kilogram (N/kg).
3Which one has different dimensions from the others?
Escape velocity is [L T⁻¹]. The other three are all [L T⁻²].
Gravitational field intensity: quick answers
What is the dimensional formula of gravitational field intensity?
The dimensional formula of gravitational field intensity is [L T⁻²]. It comes from gravitational field intensity = force / mass.
What is the SI unit of gravitational field intensity?
The SI unit of gravitational field intensity is the newton per kilogram (N/kg).
Which quantities have the same dimensions as gravitational field intensity?
Gravitational field intensity shares [L T⁻²] with acceleration, acceleration due to gravity. Equal dimensions do not make them the same quantity.