Let the symbols E, m, I and G denote energy, mass, angular momentum and gravitational constant respectively. Then figure out the dimensions of the quantity $\left(\frac{{\mathrm{El}}^2}{{\mathrm{m}}^5{\mathrm{G}}^2}\right)$.

$\left[\mathrm{E}\right]=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right],\left[\mathrm{m}\right]=\left[\mathrm{M}\right]$

$\left[l\right]=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right],\left[\mathrm{G}\right]=\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$

$\therefore \left[\frac{{\mathrm{El}}^2}{{\mathrm{m}}^5{\mathrm{G}}^2}\right]=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right)\left[{\mathrm{M}}^2{\mathrm{L}}^4{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{M}}^5\right]\left[{\mathrm{M}}^{-2}{\mathrm{L}}^6{\mathrm{T}}^{-4}\right]}$

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

As angle has no dimensions, therefore $\frac{{\mathrm{El}}^2}{{\mathrm{m}}^5{\mathrm{G}}^2}$ has the same dimensions as that of angle.