Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.
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Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

G1 Physics · Accepted Answer

Dimensions: [G] = M⁻¹L³T⁻² Therefore: [GM] = L³T⁻² For: r³/(GM) dimensions are: L³/(L³T⁻²) = T² Hence: T² = 4π²r³/(GM) is dimensionally correct.