JEE Main 2024 — Units and Dimensions Question with Solution

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 $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$ ) $\left[{\mathrm{T}}^2\right]=\frac{\left[{\mathrm{L}}^3\right]}{\left[{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]}=\left[{\mathrm{T}}^2\right]$