Dimensions of Gravitational Constant

Dimensional Formula of Gravitational Constant

The dimensional formula of gravitational constant is given by,

M-1 LT-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 LT-2.

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