If the velocity of light c , universal gravitational constant G and...

If $E$ is energy, then

\left[E\right] = \left[\dfrac{G{m}_{1}{m}_{2}}{r}\right]$</p><p>\left[E\right]\left[r\right] = \left[G{m}_{1}{m}_{2}\right]$

Since $E = \dfrac{hc}{\lambda}$

\left[\dfrac{hc}{\lambda}\right]\left[r\right] = \left[G{m}_{1}{m}_{2}\right] ⇒ \dfrac{\left[hc\right]}{\left[L\right]}\left[L\right] = \left[G\right]\left[{M}^{2}\right]$</p><p>(both$\lambda and $r$ have dimensions of length)

$∴ \left[\sqrt{\dfrac{hc}{G}}\right] = \left[M\right]$