# Dimensions of Universal Gravitational Constant

## Dimensional Formula of Universal Gravitational Constant

The dimensional formula of Universal Gravitational Constant is given by,

[M-1 LT-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Force = G × m1 × m2 × [r2]-1

Or, G = Force × r2 × [m1 × m2]-1 . . . . . (1)

Where, G = Universal Gravitational Constant

Now, the dimensions of,

Mass = [ML0 T0] . . . . (2)

Radius = [MLT0] . . . . (3)

Force = [M1 LT-2] . . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Universal Gravitational Constant = Force × r2 × [m1 × m2]-1

Or, G = [M1 LT-2] × [MLT0]2 × [M1 LT0]-1 × [M1 LT0]-1 = M-1 LT-2.

Therefore, the Universal Gravitational Constant is dimensionally represented as [M-1 LT-2].