Which of the following does not have the dimensions of velocity? (Given, \(\varepsilon_{0}=\) permittivity…
Which of the following does not have the dimensions of velocity? (Given, \(\varepsilon_{0}=\) permittivity of free space; \(\mu_{0}=\) permittivity of free space; \(v=\) frequency; \(\lambda=\) wavelength; \(P=\) pressure; \(\rho=\) density; \(k=\) wave number; and \(\omega=\) angular frequency.
\(\omega \dot{k}\)
\(v \lambda\)
\(\frac{1}{\sqrt{\varepsilon_{0} \mu_{0}}}\)
\(\sqrt{\frac{P}{\rho}}\)
Solution
Here, \(\omega \times k=T^{-1} L^{-1}\) which are not the dimensions of velocity. All others have got the dimensions of velocity.
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Asked in: JEE Mains - Units and Dimensions - Chapter Test