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Using the principle of homogunity of dimensions, check dimensionally the given equations are correct(a) \(T^2 = \frac{4π^2r^3}{G}\)(b) \(T^2 = \frac{4π^2r^3}{GM}\) |
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Answer» Here G-gravitational constant r – radius of orbit M – mass Dimensional formula for T = T Dimensional formula for r = L Dimensional formula for G = M-1 L3 T2 Dimensional formula for M = M (a) T2 M° L° = [L3 ] [M L-3 T-2 ] T2 M° L° = L° MT2 – Not correct (b) T2 = [L3 ][ML-3 T-2 ][M-1] T2 = T2 – Dimensionally correct |
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