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LL = si sept spree ae ——, , , , , , , , pasie Science : Physics 1,6 Unita and Measurementa, 4 yi NS1O MUY SEINE . FOR Whe beg ae oe BRE LAOS, Dimension (Definition) : The dimensions of physical quantity are the powers to which fundamental (base) (iii), sits eeu 08 raised to obtain the unit of a given physical quantity, units f : i, All the physical quantities can be derived from the fundamental (base) quantities. When a physical quantity Is, represented in terms of the base quantities, it can be represented as a product of different powers of the base, quantities., 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’ Pl, mass by 'M', time by 'T’ S, M, , temperature by 'K’, , current by Tl’, , luminous intensity by 'C’, , and amount of substance by 'mol’, , 1.3.1 Dimensional Formula (Equation |, , OOS eee, 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 : a, (Dimensional formula (equation) for area :, We have, Area = length x breadth = length x length = [L] x [L] = (U7, Dimensional formula (equation) for area (A) = [L? M° T°], Thus, [L? M° T°] is called dimensional formula (equation), (°°) 3 are called dimensions., Thus, dimensions of area are, 2 in length, 0 in mass L, and 0 in time, (ii) Dimensional formula (equation) for speed :, , distance length uM? 1440 <i, We have, Speed = “time "tite OM Th) MT), , Thus, [L’ M° T”] is the dimensional formula (equation) for speed., , and [’,° ~) are dimensions of speed., , Le dimensions of speed are, 1 in length, 0 in mass, , and -1 in time, , "78. ee