NEET2022PhysicsUnits and DimensionsActual
Plane angle and solid angle have:
Options
- ADimensions but no units
- BNo units and no dimensions
- CBoth units and dimensions
- DUnits but no dimensions
Correct answer
D. Units but no dimensions
Step-by-step solution
SI unit of plane angle is radian & Unit of solid angle is steradian. For dimension of plane angle: Arc length, l = r θ ⇒ θ = l r = 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 = A r 2 , where A is the area and R is the radius. Therefore, its dimensions will be, = M 0 L 2 T 0 M 0 L 2 T 0 =