What are the dimensional formulae of `omega` and K in the relation `y=Asin(omegat-Kx)`?

Options

A. `[M^(0)L^(0)T^(2)][M^(0)L^(-1)T^(0)]`
B. `[M^(0)L^(0)T^(-1)][M^(0)L^(-1)T^(0)]`
C. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(0)]`
D. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(-1)]`

Answer

b

Explanation

The argument of any trignometrical function is an angle.
`therefore (omegat-Kx)` is an angle `(theta)`. It has no dimensions.
`therefore omegat` and Kx are dimensionless.
`omegat` is dimensionless, if the dimension of `omega`
`=(1)/(T)=T^(-1)`
`therefore [omega]=[M^(0)L^(0)T^(-1)]`
Similarly, Kx will be dimensionless, if the dimension of
`K=(1)/(x)=(1)/(L)=L^(-1)`
`therefore [K]=[M^(0)L^(-1)T^(0)]`