A) \[F{{A}^{2}}T\]
B) \[FA{{T}^{2}}\]
C) \[{{F}^{2}}AT\]
D) \[FAT\]
Correct Answer: B
Solution :
Let energy \[E={{F}^{x}}{{A}^{y}}{{T}^{3}}\] Writing the dimensions on both sides \[[M{{L}^{2}}{{T}^{-2}}]={{[ML{{T}^{-2}}]}^{x}}\,{{[L{{T}^{-2}}]}^{y}}\,{{[T]}^{2}}\] \[[M{{L}^{2}}{{T}^{-2}}]=[{{M}^{x}}{{L}^{x+y}}\,{{T}^{-2x-2y+z}}]\] On comparing both sides \[x=1\] \[x+y=2\] \[\Rightarrow \] \[y=2-x=2-1=1\] and \[-2x-2y+z=-2\] \[\Rightarrow \] \[-2\times 1-2\times 1+z=-\,2\] \[\Rightarrow \] \[z=-\,2+2+2\] \[=2\] \[\therefore \] Dimensional formula of energy \[=FA{{T}^{2}}\]
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