Q. In the relation $y = a\cos{(\omega t - kx)}$, the dimensional formula for $k$ is
A) $\lbrack M^{0}L^{- 1}T^{- 1}\rbrack$
B) $\lbrack M^{0}LT^{- 1}\rbrack$
C) $\lbrack M^{0}L^{- 1}T^{0}\rbrack$
D) $\lbrack M^{0}LT\rbrack$
Explanation
$\lbrack kx\rbrack =$ Dimension of $\omega t = \$(dimensionless) Hence $K = \frac{1}{X} = \frac{1}{L} = \left\lbrack L^{- 1} \right\rbrack\ \therefore\lbrack K\rbrack = \lbrack L^{- 1}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.