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

  • [JEE MAIN 2021]
  • A

    $\left[{M}^{0} {L}^{1} {T}^{0}\right]$

  • B

    $\left[{M}^{-1} {L}^{-1} {T}^{2}\right]$

  • C

    $\left[{M}^{1} {L}^{1} {T}^{-2}\right]$

  • D

    $\left[{M}^{0} {L}^{0} {T}^{0}\right]$

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Match List$-I$ with List$-II$

List$-I$ List$-II$
$(a)$ $h$ (Planck's constant) $(i)$ $\left[ M L T ^{-1}\right]$
$(b)$ $E$ (kinetic energy) $(ii)$ $\left[ M L ^{2} T ^{-1}\right]$
$(c)$ $V$ (electric potential) $(iii)$ $\left[ M L ^{2} T ^{-2}\right]$
$(d)$ $P$ (linear momentum) $( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]$

Choose the correct answer from the options given below

  • [JEE MAIN 2021]