Question

Which of the following does not have the dimensions of velocity? (Given $ϵ$ is the permitivity of free space, ${\mu }_0$ is the permitivity of free space, v is frequency, $\lambda$ is wavelength, P is the pressure, and $\rho$ is density, k is wave number, $\omega$ is the angular frequency)

• A. $\omega k$
• B. $v\lambda$
• C. $\frac{1}{\sqrt{{ϵ}_0{\mu }_0}}$
• D. $\sqrt{\frac{P}{\rho }}$

Answer 1

The correct option is A $\omega k$

A) $\omega /k$ = $\frac{radian}{sec}\times \frac{1}{m^{-1}}$ = $\frac{radianm}{sec}$

B) $\upsilon \lambda =se{c}^{-1}meter$

C) $\frac{1}{\sqrt{{\epsilon }_0\mu }}=\frac{1}{\sqrt{\left(k{g}^{-1}{m}^{-3}{A}^2{s}^4\right)\left(kgm{A}^{-2}{s}^{-2}\right)}}=m{s}^{-1}$

D) $\sqrt{\frac{P}{\rho }}=\sqrt{\frac{kg{m}^{-1}{s}^{-2}}{kg{m}^{-3}}}=m{s}^{-1}$

Option A is correct