question_answer 43)

                  If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula                 (a) \[({{P}^{1}}\,{{A}^{-1}}\,{{T}^{1}})\]                 (b) \[({{P}^{2}}\,{{A}^{1}}\,{{T}^{1}})\]                 (c) \[({{P}^{1}}\,{{A}^{-1/2}}\,{{T}^{1}})\]             \[({{P}^{1}}\,{{A}^{1/2}}\,{{T}^{-1}})\]                

Answer:

                  (d) \[P=[ML{{T}^{-1}}]\]                 \[A=[{{L}^{2}}]\]                 or \[L={{A}^{1/2}}\]                         \[\therefore \]\[M=\frac{PT}{L}=\frac{PT}{{{A}^{1/2}}}=P{{A}^{-1/2}}T\]                         \[\therefore \] \[\text{Energy}=[M{{L}^{2}}{{T}^{-}}^{2}]=[P{{A}^{-1/2}}TA{{T}^{-2}}]\]                         \[=[P\,\,{{A}^{-1/2}}\,\,{{T}^{-1}}]\]