Question

In the expression $y=a\sin (\omega t+\theta ),$ $y$ is displacement and $t$ is the time. Write the dimensions of $\omega .$

• A. $\left[M^{0}L{T}^0\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[M^0{L}^0{T}^{-1}\right]$
• D. $\left[M^1{L}^0{T}^0\right]$

Answer 1

The correct option is C $\left[M^0{L}^0{T}^{-1}\right]$

Units for those quantities that cannot be derived from normal unit system are called supplementary quantities.

Angle is considered as a supplementary quantity.

Generally these quantities are considered as dimensionless quantities.

So $\omega$ will have the dimensions as $\left[M^0{L}^0{T}^0\right]/\left[M^0{L}^{0}T\right]=\left[T^{-1}\right]$