E,,m,,l and G denote energy, mass, angular mo | vedclass

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(a) $[E] = [M{L^2}{T^{ - 2}}],\;[m] = [M],\;[l] = [M{L^2}{T^{ - 1}}]$and $[G] = [{M^{ - 1}}{L^3}{T^{ - 2}}]$ Substituting the dimension of above quant

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(a) $[E] = [M{L^2}{T^{ - 2}}],\;[m] = [M],\;[l] = [M{L^2}{T^{ - 1}}]$and $[G] = [{M^{ - 1}}{L^3}{T^{ - 2}}]$ Substituting the dimension of above quantities in the given formula :
$\frac{{E{l^2}}}{{{m^5}{G^2}}}$$\frac{{[M{L^2}{T^{ - 2}}]\,{{[M{L^2}{T^{ - 1}}]}^2}}}{{[{M^5}]\,{{[{M^{ - 1}}{L^3}{T^{ - 2}}]}^2}}} = \frac{{{M^3}{L^6}{T^{ - 4}}}}{{{M^3}{L^6}{T^{ - 4}}}} = [{M^0}{L^0}{T^0}]$

$E,\,m,\,l$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{{E{l^2}}}{{{m^5}{G^2}}}$ are

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