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