Question

Which of the following do not have the same dimensional formula as the velocity?
(Given that ${\mu }_0=$ permeability of free space, ${ϵ}_0=$ permittivity of free space, $v=$ frequency, $\lambda =$ wavelength, $P=$pressure, $\rho =$density, $\omega =$ angular frequency, $k=$ wave number}

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

Answer 1

Answer: (D)

$\omega k$

Other than option $D$ which has the dimension $\left[\omega k\right]=\frac{1}{T}\times \frac{1}{L}=\left[L^{-1}{T}^{-1}\right]$, the dimensions of the quantities in option $A,B,C$ are of velocity $=\left[L{T}^{-1}\right]$
Hence, $\omega k$ do not have the same dimensional formula as the velocity.