Question

In the relation:
$y=a \sin (\omega t-k x)$
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)

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