Are radians and steradians the base units of SI?justify you answer.
Answers
Are radians and steradians the base units of SI?
No.
The way the question is phrased (the base units) makes it seem like there is an expectation that the radian and steradian are base units and they are the only base units (there are no others). Both aspects are incorrect.
There are 7 base units in SI: meter, kilogram, second, ampere, kelvin, mole, and candela.
Neither the radian nor steradian are SI base units. However, they are coherent derived units in SI. There are two ways commonly used to represent this:
Both have their dimensionality expressed in terms of the International System of Quantities as: L⁰M⁰T⁰I⁰Θ⁰N⁰J⁰, which corresponds to what is called either a quantity of dimension 1 or a dimensionless quantity. Consequently, both the radian and steradian are expressed in terms of derived units as:
1 m⁰ kg⁰ s⁰ A⁰ K⁰ mol⁰ cd⁰.
The factor of 1 is required to demonstrate coherence. The difficulty is how do I know that the numeric factor is indeed 1. That question leads to the second way of representation.
The radian is officially defined (SI Brochure: , Section 2.2.2, Table 3) as (1 m)/(1 m) = 1, and the steradian as (1 m²)/(1 m²) = 1. The “= 1” portion in for each corresponds to the discussion in part 1 and justifies it. The “(1 m)/(1 m)” portion for the radian comes from the [1] radian being the plane angle subtended by a circular arc of length 1m [the numerator] and radius 1 m [the denominator], based on θ = s/r. Similarly, the [1] steradian is the solid angle subtended by a portion of spherical surface of area 1 m² [numerator] and radius 1 m, which has to be squared in the definition, [denominator], based on Ω = S/r².
It does not make sense for dimensionless units to be base units. Each base unit corresponds to some non-zero mix of dimension exponents, so that all of them together form a basis set in a vector space, so each dimension is addressed. The 0-vector cannot ever be a basis vector in any vector space.
IF IT IS A HELPFUL ANSWER PLEASE MARK ME AS BRAINLIEST
hope this will help you thanks please mark me
