We will us Principle of homogeneity for solving this problem.

$\begin{array}{l}
{[\mathrm{h}]=\left[\mathrm{ML}^{2} \mathrm{~T}^{1}\right][\mathrm{c}]=\left[\mathrm{LT}^{-1}\right][\mathrm{G}]=\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right]} \\
\text { Let } \mathrm{m}=\mathrm{kc}^{\mathrm{a}} \mathrm{h}^{\mathrm{b}} \mathrm{G}^{\mathrm{c}}
\end{array}$
$\mathrm{m}=\mathrm{kc}^{1 / 2} \mathrm{~h}^{1 / 2} \mathrm{G}^{-1 / 2}=\mathrm{k} \sqrt{\mathrm{ch} / \mathrm{G}}$
Let $L=k c^{a} h^{b} G^{c}$
Solving the above we get,
$L=\mathrm{kc}^{-3 / 2} h^{1 / 2} \mathrm{G}^{1 / 2}=\mathrm{k} \sqrt{\mathrm{h} \mathrm{G} / \mathrm{c}^{3}}$
Let $T=c^{a} h^{b} G^{c}$
Solving the above we get,

$\mathrm{L}=\mathrm{kc}^{-5 / 2} h^{1 / 2} \mathrm{G}^{1 / 2}=\mathrm{k} \sqrt{h} \mathrm{G} / \mathrm{c}^{5}$