1Which of these has the same dimensions as solid angle?
Solid angle and magnification both have the dimensions [M⁰ L⁰ T⁰].
MechanicsClass 11, System of Particles and Rotational Motion
Dimensional formula of Solid angle
[M0 L0 T0]
Area on a sphere divided by radius squared, so it is dimensionless like the plane angle.
How to get the dimensional formula of solid angle
- Start from the definition: solid angle = area / area.
- area = length × length, so area is [L] × [L] = [L2].
- Put in the dimension of each part: [L2] / [L2].
- Add the powers of each base quantity: [M0 L0 T0].
Quantities with the dimensions [M⁰ L⁰ T⁰]
- Angle
- Coefficient of friction
- Coefficient of restitution
- Relative density
- Strain
- Poisson's ratio
- Reynolds number
- Emissivity
- Ratio of specific heats
- Sound level
- Relative permittivity
- Magnetic susceptibility
- Relative permeability
- Power factor
- Quality factor
- Refractive index
- Magnification
Equal dimensions do not make them the same quantity. Compare solid angle with the others in the full grid.
Three questions on solid angle
2Which of these has no dimensions at all?
Solid angle is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Impulse is [M L T⁻¹]. The other three are all [M⁰ L⁰ T⁰].
Solid angle: quick answers
What is the dimensional formula of solid angle?
The dimensional formula of solid angle is [M⁰ L⁰ T⁰]. It comes from solid angle = area / area.
What is the SI unit of solid angle?
The SI unit of solid angle is the steradian (sr).
Is solid angle dimensionless?
Yes. Solid angle is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].