Applying the principle of homogeneity of dimensions, determine...

According to principle of homogeneity dimension of LHS should be equal to dimensions of RHS so option (3) is correct. $$\begin{aligned} & \mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{\mathrm{GM}} \\ & {\left[\mathrm{T}^2\right]=\frac{\left[\mathrm{L}^3\right]}{\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right][\mathrm{M}]}} \end{aligned}$$ (Dimension of $\mathrm{G}$ is \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$)$\left[\mathrm{T}^2\right]=\frac{\left[\mathrm{L}^3\right]}{\left[\mathrm{L}^3 \mathrm{~T}^{-2}\right]}=\left[\mathrm{T}^2\right]