A) \[[{{L}^{2}}],[M{{L}^{4}}{{T}^{-2}}]\]
B) \[[L],[M{{L}^{2}}{{T}^{-2}}]\]
C) \[[M{{L}^{5}}{{T}^{-2}}],[{{L}^{3}}]\]
D) none of these
Correct Answer: C
Solution :
We know that only dimensions of similar quantities can be added or subtracted. Given, \[\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\] Dimensions of V = Dimensions of b \[[b]=[{{L}^{3}}]\] Dimensions of\[\frac{a}{{{V}^{2}}}=\]Dimensions of pressure P \[\Rightarrow \]Dimensions of\[a=\]Dimensions of\[P\times {{V}^{2}}\] Dimensions of\[[a]=[M{{L}^{-1}}{{T}^{-2}}][{{L}^{6}}]\] \[\Rightarrow \] \[[a]=[M{{L}^{5}}{{T}^{-2}}]\]
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