F=(GM1M2)/r2 find the unit and dimensions of G
The formula for gravitational force, F, is given by:
F = (G * M1 * M2) / r^2
where:
F = force
G = gravitational constant
M1 = mass of object 1
M2 = mass of object 2
r = distance between the centers of the two objects
To determine the units and dimensions of G, we can rearrange the formula as follows:
G = (F * r^2) / (M1 * M2)
The units of force (F) are Newtons (N), the units of distance (r) are meters (m), and the units of mass (M1 and M2) are kilograms (kg).
Therefore, the units of G are (N * m^2) / (kg * kg), which simplifies to:
(N * m^2) / kg^2
This means that the dimensions of G are length cubed over mass and time squared, or [L^3 / M T^2].