The dimensional formula of gravitational potential can be derived by analyzing its physical definition. Gravitational potential is a scalar quantity that represents the gravitational potential energy per unit mass at a given point in space. It is defined as the work done per unit mass to move a test mass from an infinitely far reference point to a specific point in the gravitational field.
The dimensional formula of work done is given by [M L^2 T^−2], where M represents mass, L represents length, and T represents time. The gravitational potential is defined as the work done per unit mass, so we can divide the dimensional formula of work done by the dimensional formula of mass ([M]) to obtain the dimensional formula of gravitational potential:
[M L^2 T^−2] / [M] = [L^2 T^−2].
Therefore, the dimensional formula of gravitational potential is [L^2 T^−2], where L represents length and T represents time.