Dimensions of Physical Quantities

Most physical quantities can be expressed in terms of five basic dimensions:

  1. Mass (M)
  2. Length (L)
  3. Time (T)
  4. Electrical current (I)
  5. Temperature (θ)

Dimensional Formula

Dimensions of the physical quantities are combinations of the powers of M, L and T. For example,

  • Volume requires 3 measurements in length. So it has 3 dimensions in length. Its dimensional formula is L3.
  • Density is mass divided by volume. Its dimensional formula is ML–3.
  • Speed is distance traveled in unit time or length divided by time. Its dimensional formula is LT–1.
  • Acceleration is change in velocity per unit time, i.e., length per unit time per unit time. Its dimensionsal formula is LT–2.
  • Force is mass multiplied by acceleration. Its dimensions are given by the formula MLT–2.

Dimensional Analysis

Dimensional analysis is the process of checking the dimensions of a quantity, or a combination of quantities. One of the important principles of dimensional analysis is that each physical quantity on the two side of an equation must have the same dimensions. Thus, if x = p + q, then p and q will have the same dimensions as x. This helps in checking the accuracy of equations, or getting the dimensions of a quantity using an equation.