A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{5}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{-5}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{5}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{-1}}}{{\text{L}}^{5}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
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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