Answer:
(i) \[{{T}^{2}}=4{{\pi }^{2}}{{r}^{2}}\] Dimensionally, \[{{M}^{0}}{{L}^{0}}{{T}^{2}}={{M}^{0}}{{L}^{2}}{{T}^{0}}\] As LHS \[\ne \]RHS, the formula is incorrect. (ii) \[{{T}^{2}}=\frac{4{{\pi }^{2}}{{r}^{3}}}{G}\] Dimensionally, \[{{M}^{0}}{{L}^{0}}{{T}^{2}}=\frac{{{L}^{3}}}{{{M}^{-1}}{{L}^{3}}{{T}^{-2}}}={{M}^{1}}{{L}^{0}}{{T}^{2}}\] As LHS \[\ne \] RHS, the formula is incorrect (iii) \[{{T}^{2}}=\frac{4{{\pi }^{2}}{{r}^{3}}}{GM}\] Dimensionally, \[{{M}^{0}}{{L}^{0}}{{T}^{2}}=\frac{{{L}^{3}}}{{{M}^{-1}}{{L}^{3}}{{T}^{-2}}M}={{M}^{0}}{{L}^{0}}{{T}^{2}}\] As LHS \[=\] RHS, the formula is correct.
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