A) \[[M{{L}^{5}}{{T}^{-1}}]\]
B) \[[M{{L}^{-5}}{{T}^{-1}}]\]
C) \[[M{{L}^{5}}{{T}^{-2}}]\]
D) \[[{{M}^{-1}}{{L}^{5}}{{T}^{2}}]\]
Correct Answer: C
Solution :
Key Idea: According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same. We have given \[\left( p+\frac{a}{{{V}^{2}}} \right)\,(V-b)=RT\] According to principle of homogeneity, \[[p]=\left[ \frac{a}{{{V}^{2}}} \right]\] or \[[a]=[p]\,[{{V}^{2}}]\] or \[[a]=[M{{L}^{-1}}{{T}^{-2}}]\,[{{L}^{6}}]\] \[\therefore \] \[[a]=[M{{L}^{5}}{{T}^{-2}}]\] Note : The physical quantities separated by the symbols +, - , =, > , < etc., have the same dimensions.
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