What is the dimension of gravitational constant?

The universal gravitational constant (G) is derived from Newton's Law of Universal Gravitation, which states that the force (F) between two masses is F = G(m1*m2)/r². To find the dimensions of G, the formula is rearranged as G = Fr²/m1m2. The dimensional formula for force (F) is [MLT⁻²], for distance squared (r²) is [L²], and for the product of two masses (m1m2) is [M²]. Substituting these into the equation gives G = [MLT⁻²][L²] / [M²], which simplifies to [M⁻¹L³T⁻²] [1]. This indicates that G has dimensions of inverse mass, length cubed, and inverse time squared. While the provided options contain typographical errors (using 'Z' or '?' instead of '3' and '~' for negative signs), Option 2 (M⁻¹L³T⁻²) is the standard scientific representation for the dimensions of G [1].

Sources

1. [1] https://www.britannica.com/science/gravitational-constant