Answer to Question #141169 in Mechanics | Relativity for Nama Glory

Question #141169
Show that fo = 1/2l[sqrt(T/u)] is homogenous
1
Expert's answer
2020-11-10T07:08:58-0500

Given equation is, fo=12LTμf_o = \frac{1}{2L}\sqrt{\frac{T}{\mu}}

where f0f_0 is frequency, L is the length, T is the tension and μ\mu is mass per unit length.


Equation is homogeneous only when dimensions on the both sides are eqaul.

Dimension of the left hand side, [T1][T^{-1}]


Dimension of the right hand sides,

1[L][MLT2][ML1]=1[L][L2T2]=[LT1][L]=[T1]\frac{1}{[L]}\sqrt{\frac{[MLT^{-2}]}{[ML^{-1}]}} = \frac{1}{[L]}\sqrt{[L^2T^{-2}]} = \frac{[LT^{-1}]}{[L]} = [T^{-1}]



Since, dimension of the both sides are equal so the equation is homogeneous.




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