1.

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

Answer»

`T=2pisqrt(R^(3))/(GM)`
`T=2pi SQRT(GM)/R^(3)`
`T=2pi sqrt(GM)/(R^(2))`
`T=2pi sqrt(R^(2)/(GM)`

Solution :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))`


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