Question

State the principle of homogeneity. test the dimensional homogeneity of equations— s = ut +1/2 at2

Answer 1

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♦ Units and Dimensions ♦

 • Principle of Homogeneity : Dimensions of expressions on either sides of a         dimensional equation are same 

 • Homogeneity Test : 
     
    [tex] s = [ M^0L^1T^0] \ ; \\ \\ ut + ( 1/2 )at^2 = [M^0L^1T^{-1}] [M^0L^0T^1] + [M^0L^1T^{-2}][M^0L^0T^{2}] \\ \ \ \ \ \ \ = [M^0L^1T^{-1+1}]+ [M^0L^1T^{-1+1}] \\ = [M^0L^1T^0][/tex]

Since we find that the Dimensional Formulas for both sides are equivalent, the homogeneity of equation is satisfied and hence, the equation is dimensionally correct 
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For further doubts concerning Dimensions and Homogeneity  :
 ○ https://www.sciencetopia.net/physics/dimensional-equation-formula
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Hope that helps