Physics - Unit & Dimension Question with Solution | TestHub

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