Dimensional Formula for Gravitational Constant

The dimensional formula of gravitational constant is

M^-1 L³ T ^-2

where M denotes mass, L denotes length, and T denotes time.

Derivation of Dimensional Formula for Gravitational Constant

We can derive the dimensional formula for gravitational constant as follow:

As we know, from Newton’s law of gravitation,

Force (F) = (Gm₁m₂) × r^-2

Gravitational Constant (G) = F × r² × (m₁m₂)^-1 ……(1)

As, Force (F) = Mass × Acceleration

Dimensionally, Force (F) = 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 × [m₁ m₂]^-1

G = [M¹ L¹ T^-2] × [L]² × [M]^-2

G = [M^-1 L³ T^-2]

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

Dimensional Formula for Gravitational Constant is [M^-1 L³ T^-2]. The Gravitational Constant is represented by ‘G‘. It is Newton’s gravitational constant and gives the constant of proportionality in Newton’s Universal law of gravitation which is the basis of our understanding of non-relativistic gravity.

In this article, we will discuss the ‘Gravitational Constant,’ its unit, dimensional formula, and the derivation of the Gravitational Constant.