Check the dimensional consistency of the following u=(1/2L)root f/m.. L= length, u= frequency, f= force, m= mass/unit length, u is the velocity

Answers (1)
S safeer

Dimension of LHS

[u]=LT^{-1}

Dimension of RHS

[\frac{1}{2L}\sqrt{\frac{F}{m}}]=\frac{1}{L}\sqrt{\frac{MLT^{-2}}{\frac{M}{L}}}\\\\=\frac{1}{L}\sqrt{L^2T^{-2}}=T^{-1}

The dimension of LHS not equal to RHS. 

So the equation is dimensionally inconsistent. 

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