Question

The unit of plane angle is radian, hence its dimensions are

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

Answer 1

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

Arc length $l=r\theta$

$\theta =\frac{l}{r}$

Since $\theta$ is a ratio of two quantities of the same dimension, it is dimensionless. So the unit is $\left[M^0{L}^0{T}^0\right]$