Question

In the relation:
$y=a\sin (\omega t-kx)$
the dimensional formula for $\mathrm{k}$ is:

• A. $\left[{\mathrm{M}}^0\mathrm{LT}\right]$
• B. $\left[{\mathrm{M}}^0{\mathrm{L}}^{-1}{\mathrm{T}}^0\right]$
• C. $\left[{\mathrm{M}}^0{\mathrm{LT}}^{-1}\right]$
• D. $\left[{\mathrm{M}}^0{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\right]$

Answer 1

Answer: (B)

$\begin{array}{rl}& \text{ Here; }\mathrm{kx}\text{ is dimensionless. Hence, }\\ & [\mathrm{k}]=\left[\frac{2\pi }{\lambda }\right]=\left[{\mathrm{M}}^0{\mathrm{L}}^{-1}{\mathrm{T}}^0\right]\end{array}$