1Which of these has the same dimensions as acceleration due to gravity?
Acceleration due to gravity and gravitational field intensity both have the dimensions [L T⁻²].
GravitationClass 11, Gravitation
Dimensional formula of Acceleration due to gravity
[L T-2]
The acceleration of a falling body, GM/R² at the surface. It has the dimension of any acceleration.
How to get the dimensional formula of acceleration due to gravity
- Start from the definition: acceleration due to gravity = gravitational constant × mass / length2.
- 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].
- Put in the dimension of each part: [M-1 L3 T-2] × [M] / [L]2.
- 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 acceleration due to gravity with the others in the full grid.
Three questions on acceleration due to gravity
2What is the SI unit of acceleration due to gravity?
The SI unit of acceleration due to gravity is the metre per second squared (m/s²).
3Which one has different dimensions from the others?
Escape velocity is [L T⁻¹]. The other three are all [L T⁻²].
An equation that uses acceleration due to gravity
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
T = 2 π sqrt(l / g)T[T]=2 pi sqrt(l/g)[T]Dimensionally consistentEvery term is [T]
l = lengthg = acceleration due to gravity
Acceleration due to gravity: quick answers
What is the dimensional formula of acceleration due to gravity?
The dimensional formula of acceleration due to gravity is [L T⁻²]. It comes from acceleration due to gravity = gravitational constant × mass / length².
What is the SI unit of acceleration due to gravity?
The SI unit of acceleration due to gravity is the metre per second squared (m/s²).
Which quantities have the same dimensions as acceleration due to gravity?
Acceleration due to gravity shares [L T⁻²] with acceleration, gravitational field intensity. Equal dimensions do not make them the same quantity.