Question

From the dimensional consideration, which of the following equation is correct
A. `T=2pisqrt(R^(3)/(GM)`
B. `T=2pisqrt((GM)/(R^(3))`
C. `T=2pisqrt((GM)/(R^(2))`
D. `T=2pisqrt((R^(2))/(GM)`

Answer 1

Correct Answer - A
Taking, `T=2pisqrt((R^(3))/(GM)`
Substituting the dimensions, LHS = [T]
RHS `2pi|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))`