Plane angle and solid angle have:NEET 2022 (Phase 1)

Question

TestHub · Accepted Answer

SI unit of plane angle is radian & Unit of solid angle is steradian.

For dimension of plane angle:

Arc length, $l = r θ$

$\Rightarrow θ = \frac{l}{r} = \frac{[M^{0} L^{1} T^{0}]}{[M^{0} L^{1} T^{0}]} = [M^{0} L^{0} T^{0}]$

Clearly, it is a ratio of two quantities of the same dimension, hence it is dimensionless.

For dimension of solid angle:

Solid angle can be considered as a 3D analogue of a plane angle. It is given by the equation,

$Ω = \frac{A}{r^{2}}$ , where $A$ is the area and $R$ is the radius.

Therefore, its dimensions will be, $= \frac{[M^{0} L^{2} T^{0}]}{[M^{0} L^{2} T^{0}]} = [M^{0} L^{0} T^{0}]$ , hence it is also dimensionless.

Physics - Unit & Dimension Question with Solution | TestHub