If the speed v of a particle of mass m as function of time t is given by `v=omegaAsin[(sqrt(k)/(m))t]`, where A has dimension of length.

Options

A. The argement of trigonometric function must be a dimensionless quantity
B. Dimensional formula of `omega` is `LT^(-1)`
C. Dimensional formula of `k` is `MLT^(-1)`
D. Dimensional formula of `sqrt(k)/(m)` is `T`

Answer

a

Explanation

Plane angle is dimensionless
`[omega A] = [v]`
`[omega] L = t^(-1)`
[omega] = T^(-1)`
[omega] = T^(-1)`
`[sqrt((k)/(m)t)]= M^(0)L^(0)T^(0)`
`[k] = ([m])/([t^(2)]) = MT^(-1)`
`[sqrt((k)/(m))] = M^(0)L^(0)T^(0) rArr [sqrt((k)/(m))]= T^(-1)`