If `v = alpha sin (betat)` where v is meter per second and t is in second then. Find sum of dimesions with respect to the time of `alpha` and `beta`

Options

A. 1
B. `-1`
C. 2
D. `-2`

Answer

D

Explanation

`v = alpha sin (beta t)`
By dimensional homogenity `alpha` has same dimension of `v = [LT^(-1)] sin (betat)` and `sin (beta t)` no dimension as it is trgonometric function
`alpha = M^(0)L^(1)T^(-1)`
`beta = M^(0)L^(0)T^(-1)`
so w.r.t. = dimensions are `(-1) + (-1) = -2`