From the dimensional consideration,which of t | vedclass

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(A) To check the dimensional consistency of the equation $T = 2\pi \sqrt {\frac{{{R^3}}}{{GM}}} $:$1$. The dimension of time period $T$ is $[T]$.$2$.

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

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(A) To check the dimensional consistency of the equation $T = 2\pi \sqrt {\frac{{{R^3}}}{{GM}}} $:$1$. The dimension of time period $T$ is $[T]$.$2$. The dimension of radius $R$ is $[L]$. So,$R^3$ has dimensions $[L^3]$.$3$. The gravitational constant $G$ has dimensions $[M^{-1}L^3T^{-2}]$.$4$. The mass $M$ has dimensions $[M]$.$5$. The product $GM$ has dimensions $[M^{-1}L^3T^{-2}] 	imes [M] = [L^3T^{-2}]$.$6$. Substituting these into the expression under the square root: $\sqrt{\frac{R^3}{GM}} = \sqrt{\frac{L^3}{L^3T^{-2}}} = \sqrt{T^2} = [T]$.$7$. Since the dimensions of the left-hand side and right-hand side match,the equation is dimensionally correct.

From the dimensional consideration,which of the following equations is correct?

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