Question

In the relation ` y = r sin ( omega t - kx)`, the dimensions of `omega//k` are
A. `[M^(0) L^(0) T^(0)]`
B. `[M^(0) L^(1) T^(-1)]`
C. `[M^(0) L^(0) T^(1)]`
D. `[M^(0) L^(1) T^(0)]`

Answer 1

Correct Answer - B
`y = r sin ( omega t - kx)`
Here `omega t = angle rArr omega = (1)/(T) = T^(-1)`
Similarly , `kx = angle rArr K = (1)/(x) = L^(-1)` :. (omega)/(k) = (T^(-1))/(L^(-1)) = LT^(-1)`
Or simply `omega//k` represents wave velocity.
`(omega)/(k) = ( 2 pi f)/( 2 pi//f) = f lambda = v` , where f is frequency.