Question

In the relation: $\frac{d y}{d x}=2\omega sin\left(\omega t + \phi_{0}\right)$ the dimensional formula for $\left(\omega t + \phi_{0}\right)$ is :

• A. $\left[MLT\right]$
• B. $\left[MLT^{0}\right]$
• C. $\left[ML^{0} T^{0}\right]$
• 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, $\left(\omega t + \phi_{0}\right)$ is dimensionless because it is an argument of a trigonometric function.
Unit of an angle is radian, it is a dimension less quantity
So $\left(\omega \text{t} + \phi_{0}\right)$ is dimensionless.