If \({E}, {L}, {m}\) and \({G}\) denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of \({P}\) in the formula \({P}={EL}^{2} {m}^{-5} {G}^{-2}\) are

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(D) \(\left[{M}^{0} {L}^{0} {T}^{0}\right]\)

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\({E}={ML}^{2} {T}^{-2}\)

\({L}={ML}^{2} {T}^{-1}\)

\({m}={M}\)

\({G}={M}^{-1} {L}^{+3} {T}^{-2}\)

\({P}=\frac{{EL}^{2}}{{M}^{5} {G}^{2}}\)

\({[{P}]=\frac{\left({ML}^{2} {T}^{-2}\right)\left({M}^{2} {L}^{4} {T}^{-2}\right)}{{M}^{5}\left({M}^{-2} {L}^{6} {T}^{-4}\right)}={M}^{0} {L}^{0} {T}^{0}}\)

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