The function `f` is given by `f = A sin alpha x + B cos beta t`, where `x` is displacement and `t` is the time. The dimensions of `alpha//beta` is

Options

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

Answer

C

Explanation

(3) Angles have no dimension.
`alpha x` is dimensionless : `[alpha] = L^(-1)`
`beta t` is dimensionless : `[beta] = T^(-1)`
`(alpha)/(beta) = (L^(-1))/(T^(-1)) = L^(-1) T`