Find the units and dimensions of 'G' the gravitational constant in the following equation, F=(GM2M1/r squared where F is the force of attraction between the two bodies of mass respectively.

Question

And r is the separation distance before the two bodies

Answer 1

The units and dimensions of the gravitational constant, G, can be found by analyzing the given equation.

In the equation, F = (GM1M2/r^2), F represents force, which has the unit of Newtons (N).

The masses, M1 and M2, have the unit of kilograms (kg).

The separation distance, r, is given in meters (m).

Therefore, we can express the equation as:
[N] = [G] * [kg] * [kg] / [m^2]

To find the units of G, we can rearrange the equation:
[G] = [N] * [m^2] / ([kg] * [kg])

Simplifying further:
[G] = [N] / [kg^2] * [m^2]

Therefore, the units of G, the gravitational constant, are:
[N] / [kg^2] * [m^2]

The dimensions of G are derived from the units:
Dimension of G = (dimension of N) / (dimension of kg^2) * (dimension of m^2)

The dimension of N is [M][L][T]^-2 (mass times length divided by time squared).
The dimension of kg is [M] (mass).
The dimension of m^2 is [L]^2 (length squared).

Substituting in the dimensions, we get:
Dimension of G = ([M][L][T]^-2) / ([M]^2) * ([L]^2)

Simplifying further:
Dimension of G = [M]^-1 * [T]^-2 * [L]^0

So, the dimensions of G are:
[M]^-1 * [T]^-2 * [L]^0