1.3 DIMENSIONS DIMENSIONAL FORMULA Dimension (Definition) : The dimensions of physical quantity are the powers to which fundamental (base) units must be raised to obtain the unit of a given physical quantity. Dimension : The exponent of a base quantity which enters into the expression, is called dimension of the quantity in that base. To decide the dimensions of physical quantity, the units of fundamental quantities are expressed by the following : length can be expressed by 'L' mass by 'M' time by 'T'

1.3.1 Dimensional Formula (Equation) Dimensional formula (equation) (Definition) : An equation, which gives the relation between fundamental units and derived units in terms of dimensions is called dimensional formula (equation). In mechanics the length, mass and time are taken as three base dimensions and are represented by letters L, M, T respectively. The derived unit of all physical quantities can be represented in terms of the base (fundamental) unit of length, mass and time raised to some power (exponent). Examples : (i) Dimensional formula (equation) for area : We have, Area = length  breadth = length  length = [L]  [L] = [L2]  Dimensional formula (equation) for area (A) = [L2 M0 T0] Thus, [L2 M0 T0]  is called dimensional formula (equation) [2, 0, 0]  are called dimensions. Thus, dimensions of area are 2 in length 0 in mass and 0 in time

Physical quantities with formula, dimensional formula and SI unit symbols :

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Basic Science : Physics 1.2 Units and Measurements

Table 1.6 Sr. Physical Formula or Relation Dimensional S.I. unit No. quantity formula symbol (equation) 1. Length length [L1 M0 T0] m 2. Mass mass [L0 M1 T0] kg 3. Time time [L0 M0 T1] s 4. Area length  breadth = length  length [L2 M0 T0] m2 5. Volume length  breadth  height [L3 M0 T0] m3 = length  length  length 6. Density mass mass = volume length  breadth  height mass [L3 M1 T0] kg/m3 = length  length  length 7. Speed distance length [L1 M0 T1] m/s = (velocity) time time distance 8. Acceleration velocity time [L1 M0 T2] m/s2 = time time 9. Force velocity mass  acceleration = mass  time [L1 M1 T2] N  distance  time  (kg.m/s2) = mass     time 