Since, LHS = RHS, the given formula is verified dimensionally.įAQs on Dimensional Formula What Is Meant By Dimensional Formula? The formula for acceleration is given as, a = change in velocity/time taken = ∆V/∆tĪcceleration = change in velocity/time takenĭimesional formula for RHS = / = Solution:Īnswer: Dimensional formula for momentum = Įxample 3: State and verify the formula for acceleration using the dimensional analysis. Solution:Ĭomparing with dimensional formula, we get,Įxample 2: Find the dimensional formula of momentum. Examples Using Dimensional FormulasĮxample 1: Using dimensional formula, Q = M aL bT c, find the values of a, b, and c if the given quantity is velocity. Let us have a look at a few solved examples to understand the dimensional formula better. It expresses one quantity in terms of the fundamental units.For conversion from one system of units into another system for any given quantity.The dimensional formula helps in deriving the relationship between different physical quantities.It is used to verify the correctness of an equation.The dimensional formula finds applications in the following cases, ⇒ Dimensional formula (equation) for area (A) = Applications of Dimensional Formula An example of a dimensional equation is as given below, The dimensional formula of individual quantities is used to establish a relationship between them in any dimensional equation. In mechanics, the length, mass, time, temperature, and electric current are taken as three base dimensions, and meter, kilogram, second, ampere, kelvin, mole, and candela are the fundamental units. Inductance (L) (energy = \(\frac\right)\)ĭimensional Formula and Dimensional EquationsĪ dimensional equation is an equation that relates fundamental units and derived units in terms of dimensions. ![]() The following table shows dimensional formulas for different physical quantities: Physical quantityĪcceleration or acceleration due to gravityĪngular frequency (angular displacement/time)Ĭoefficient of linear or areal or volume expansionĬoefficient of surface tension (force/length)Ĭoefficient of viscosity (F = η × A × (dv/dx))Įlectric charge or quantity of electric charge (current × time)Įlectric dipole moment (charge × distance)Įlectric field strength or Intensity of electric field (force/charge)Įlectric resistance (potential difference/current)Įmf (or) electric potential (work/charge)įorce constant or spring constant (force/extension) Where, M, L, T are base dimensions mass, length, and time respectively and a, b and, c are their respective exponents. The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by, Dimensional Formula: The concept of dimension in maths does not have any specific dimensional formula. Dimension of any physical quantity is the power to which the fundamental units are raised to obtain one unit of that quantity. Let us learn about the dimensional formula with a few examples in the end. ![]() Before learning the dimensional formula, let us recall what is dimension. Dimension in maths is a measure of the length, width, or height extended in a particular direction. By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.
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