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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
$\left[{M}^{0} {L}^{1} {T}^{0}\right]$
$\left[{M}^{-1} {L}^{-1} {T}^{2}\right]$
$\left[{M}^{1} {L}^{1} {T}^{-2}\right]$
$\left[{M}^{0} {L}^{0} {T}^{0}\right]$
Solution
${E}={ML}^{2} {T}^{-2}$
${L}={ML}^{2} {T}^{-1}$
${m}={M}$
${G}={M}^{-1} {L}^{+3} {T}^{-2}$
${P}=\frac{{EL}^{2}}{{M}^{5} {G}^{2}}$
${[{P}]=\frac{\left({ML}^{2} {T}^{-2}\right)\left({M}^{2} {L}^{4} {T}^{-2}\right)}{{M}^{5}\left({M}^{-2} {L}^{6} {T}^{-4}\right)}={M}^{0} {L}^{0} {T}^{0}}$
Similar Questions
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
List $I$ | List $II$ |
$P.$ Boltzmann constant | $1.$ $\left[ ML ^2 T ^{-1}\right]$ |
$Q.$ Coefficient of viscosity | $2.$ $\left[ ML ^{-1} T ^{-1}\right]$ |
$R.$ Planck constant | $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$ |
$S.$ Thermal conductivity | $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$ |
Codes: $ \quad \quad P \quad Q \quad R \quad S $