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LEGENDS (MON) One ee, , , , , , , _Dimensional Analysis, Analyzing any equat, dimensional analysis., , Af peipications of Dimensional analysis, mensional analysis is used, 1. To check the correctness of an equation., , 2. To derive the relation between various physical quantities., 3. To convert unit of a given physical quantity from one system to, , another., , ion by the method of dimensions is called as, , , , , Principle of homogeneity or consistency, , Statement:, All the terms on both sides of the physical equation must have same, , dimensions., , , , , , , , Check the correctness of an equation x = ut + 2 at? by the method, , of dimensions. Where x is the displacement of the body , vu is its, velocity, a is acceleration and t is the time, , , , , , Given equation is x =ut+ 1a }* —----.-= > (1), , , , Express the derived quantities in terms of fundamental quantities and, neglect the constants., , , , , , We have, u= v =, , , , Write the dimensions on both sides in terms of MLT, , => [M°L! T?] = [M°L'T?] + [M°L'T?], LHS = RHS, From principle of homogeneity, the given equation in dimensionally correct., , , , , Check the correctness of an equation ‘2 my* = mgh by the method of, _Alimensions. Where m is the mass of the body , v is its velocity, g is, _ acceleration due to gravity and h is the height, , , , , , Express the derived quantities in terms of fundamental, eglect the constants. _