Dimensions of Gravitational Constant

Dimensional Formula of Gravitational Constant

The dimensional formula of gravitational constant is given by,

M^-1 L³ T^-2

Where,

• M = Mass
• L = Length
• T = Time

Derivation

From Newton’s law of gravitation,

Force (F) = [GmM] × r^-2

Gravitational Constant (G) = F × r² × [Mm]^-1  . . . . (1)

Since, Force (F) = Mass × Acceleration = M × [LT^-2]

∴ The dimensional formula of force = M¹ L¹ T^-2 . . . . (2)

On substituting equation (2) in equation (1) we get,

Gravitational Constant (G) = F × r² × [Mm]^-1

Or, G = [M¹ L¹ T^-2] × [L]² × [M]^-2 = [M^-1 L³ T^-2].

Therefore, the gravitational constant is dimensionally represented as M^-1 L³ T^-2.

⇒ Check Other Dimensional Formulas:

• Dimensions of Gravitational Potential Energy
• Dimensions of Temperature
• Dimensions of Linear Momentum
• Dimensions of Boltzmann Constant
• Dimensions of Permittivity

Gravitation