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

Options

A. `T=2pisqrt(R^(3))/(GM)`
B. `T=2pi sqrt(GM)/R^(3)`
C. `T=2pi sqrt(GM)/(R^(2))`
D. `T=2pi sqrt(R^(2)/(GM)`

Answer

A

Explanation

Taking, `T=2pi sqrt(R3)/(GM)` substituting the dimensions, `LHS=[T]RHS2pi|sqrt(R^(3)/(GM))|=sqrt([L]^(3)/([M^(-1)L^(3)T^(-2)][M]))=sqrt([T]^(2))=[T]`
`Thus, LHS=RHS for `T=2pisqrt(R^(3)/(GM))`