Question

In the relation: $\frac{dy}{dx}=2\omega sin\left(\omega t+{\varphi }_0\right)$ the dimensional formula for $\left(\omega t+{\varphi }_0\right)$ is :

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

Answer 1

Answer: (D)

The unit of angle is radian which is dimensionless quantity. So, here, $\left(\omega t+{\varphi }_0\right)$ is dimensionless because it is an argument of a trigonometric function.
Unit of an angle is radian, it is a dimension less quantity
So $\left(\omega \text{t}+{\varphi }_0\right)$ is dimensionless.