A) \[[ML{{T}^{-1}}]\]and\[[ML{{T}^{0}}]\]
B) \[[ML{{T}^{-3}}]\]and\[[M{{L}^{2}}{{T}^{4}}]\]
C) \[[ML{{T}^{-4}}]\]and\[[ML{{T}^{1}}]\]
D) \[[ML{{T}^{-3}}]\]and\[[ML{{T}^{-4}}]\]
Correct Answer: D
Solution :
Key Idea: Every equation relating physical quantity should be in dimensional balance. Given, equation \[F=at+b{{t}^{2}}\] Only similar quantities can be equated, hence dimensions of the terms on both sides of the equation must be same. \[[ML{{T}^{-2}}]=a[T]\] \[\Rightarrow \] \[a=[ML{{T}^{-3}}]\] Similarly \[[ML{{T}^{-2}}]=b{{[T]}^{2}}\] \[\Rightarrow \] \[b=[ML{{T}^{-4}}]\] Note: The physical quantities separated by the symbols +, -. =, >, < etc. have the same dimensions.
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