A) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{-2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]
C) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]
Correct Answer: D
Solution :
Key Idea: Every equation relating physical quantities should be in dimensional balance. The given equation is \[n=\frac{A+B}{{{\lambda }^{2}}}\] where A and B are constants. The dimensions of all the terms on both sides should be same i.e., \[[B]=[A]=[n{{\lambda }^{2}}]\] \[\therefore \] \[[B]=[{{M}^{o}}{{L}^{o}}{{T}^{o}}][{{L}^{2}}]\] \[=[{{M}^{o}}{{L}^{2}}{{T}^{o}}]\]
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