1Which is the dimensional formula of gravitational constant?
Gravitational constant works out to [M⁻¹ L³ T⁻²].
Fundamental constantsClass 11, Gravitation
Dimensional formula of Gravitational constant
[M-1 L3 T-2]
The constant G in F = Gm1m2/r². Do not confuse it with g, the acceleration due to gravity.
How to get the dimensional formula of gravitational constant
- Start from the definition: gravitational constant = force × length2 / mass2.
- 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]2 / [M]2.
- Add the powers of each base quantity: [M-1 L3 T-2].
Three questions on gravitational constant
2What is the SI unit of gravitational constant?
The SI unit of gravitational constant is the newton metre squared per kilogram squared (N m²/kg²).
3Do gravitational constant and permeability of free space have the same dimensions?
Gravitational constant is [M⁻¹ L³ T⁻²] but permeability of free space is [M L T⁻² A⁻²].
An equation that uses gravitational constant
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
F = G m1 m2 / r2F[M L T-2]=G m1 m2 / r2[M L T-2]Dimensionally consistentEvery term is [M L T-2]
r = length
Gravitational constant: quick answers
What is the dimensional formula of gravitational constant?
The dimensional formula of gravitational constant is [M⁻¹ L³ T⁻²]. It comes from gravitational constant = force × length² / mass².
What is the SI unit of gravitational constant?
The SI unit of gravitational constant is the newton metre squared per kilogram squared (N m²/kg²).
Is gravitational constant dimensionless?
No. Gravitational constant has the dimensions [M⁻¹ L³ T⁻²].