Dimensional Formula of Universal Gravitational Constant

The dimensional formula of Universal Gravitational Constant is given by,

[M^-1 L³ T^-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 = [M¹ L⁰ T⁰] . . . . (2)

Radius = [M⁰ L¹ T⁰] . . . . (3)

Force = [M¹ L¹ T^-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 L¹ T^-2] × [M⁰ L¹ T⁰]² × [M¹ L⁰ T⁰]^-1 × [M¹ L⁰ T⁰]^-1 = M^-1 L³ T^-2.

Therefore, the Universal Gravitational Constant is dimensionally represented as [M^-1 L³ T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Gravitational Potential Energy
• Dimensions of Displacement
• Dimensions of Reynolds Number
• Dimensions of Velocity Gradient
• Dimensions of Bulk Modulus