From the dimensional consideration, which of the following equation is correct

(1) $T=2\pi \sqrt{\frac{{R}^{3}}{GM}}$

(2) $T=2\pi \sqrt{\frac{GM}{{R}^{3}}}$

(3) $T=2\pi \sqrt{\frac{GM}{{R}^{2}}}$

(4) $T=2\pi \sqrt{\frac{{R}^{2}}{GM}}$

(1) By substituting the dimensions in $T=2\pi \sqrt{\frac{{R}^{3}}{GM}}$

we get $\sqrt{\frac{{L}^{3}}{{M}^{-1}{L}^{3}{T}^{-2}×M}}=T$

Difficulty Level:

• 37%
• 25%
• 31%
• 9%