The dimensional formula of a physical quantity expresses how its units are derived from the fundamental units of mass (M), length (L), and time (T). In the International System of Units (SI), the dimensional formulas for mass, length, and time are as follows:
Mass (M): [M]
Length (L): [L]
Time (T): [T]
In dimensional analysis, square brackets "[ ]" are used to denote the dimensions of a quantity. The dimensions of mass, length, and time are considered fundamental and are not derived from other physical quantities.
For example, if we want to express velocity, which is the ratio of length to time, its dimensional formula would be:
Velocity: [L]/[T]
Similarly, for quantities such as area, volume, force, energy, or any other physical quantity, their dimensional formulas can be derived based on the fundamental dimensions of mass, length, and time.