Gravitational constant, denoted by G, is a fundamental constant in physics that appears in Newton's law of universal gravitation and Einstein's theory of general relativity. It determines the strength of the gravitational force between two objects with mass.

To find the dimension formula of gravitational constant, we need to analyze the dimensions of the quantities involved. Let's consider the dimensions of energy (E), length (L), and time (T) first.

1. Energy (E):
The dimension of energy can be expressed as [M][L]^2[T]^-2, where [M] represents the dimension of mass, [L] represents the dimension of length, and [T] represents the dimension of time.

2. Length (L):
The dimension of length is denoted by [L].

3. Time (T):
The dimension of time is denoted by [T].

Next, let's consider Newton's law of universal gravitation, which states that the gravitational force (F) between two objects with masses (m1 and m2) separated by a distance (r) is given by:

F = G * (m1 * m2) / r^2

From this equation, we can deduce the dimensions of gravitational constant (G).

1. Dimensions of force (F):
The dimension of force is given by [M][L][T]^-2.

2. Dimensions of mass (m1 and m2):
The dimension of mass can be denoted by [M].

3. Dimensions of distance (r):
The dimension of distance is denoted by [L].

Since the force, mass, and distance in the equation have dimensions, the gravitational constant must have dimensions that balance the equation. Therefore, the dimension formula for the gravitational constant (G) can be found by equating the dimensions:

[M][L][T]^-2 = G * [M] * [M] / [L]^2

Simplifying the equation, we get:

[M][L][T]^-2 = [M]^2 * G / [L]^2

Comparing the dimensions on both sides, we find:

1. Dimensions of mass:
[M] = [M]^2

This implies that the dimension of mass is [M]^2.

2. Dimensions of length:
[L] = [L]^2

This implies that the dimension of length is [L]^2.

3. Dimensions of time:
[T]^-2 = G / [L]^2

This implies that the dimension of time is [T]^-2.

Therefore, the dimension formula for the gravitational constant is [M]^-1 * [L]^3 * [T]^-2.

In conclusion, the dimension formula for the gravitational constant (G) is [M]^-1 * [L]^3 * [T]^-2.