Explain supplementary quantities and their unit of SI system.

Explanation

There are two supplementary quantities of SI system.
(1) Plane angle `d theta(2)` Solid angle `d Omega`
(1) Plane angle `d theta` : Ratio of arc of circle and radiusof circle is called plane angle `(d theta)`

From figure plane angle `d theta=("arc")/("radius")(AB)/(r)=(ds)/(r)`
Plane angle subtended at centre by arc of circle having length equal to radius is called 1 radian. It is represented as rad. Maximum value of plane angle is `2pi` rad
If AB= r then `theta=1` rad
`[1^(@)=(pi)/(180) "rad"] and [1 rad=(180)/(pi)` degree]
(2) Solid angle ` dOmega:` d by area `(DeltaA)` on spherical surface with centre of sphere is called solid angle `dOmega`

From figure,
Solid angle `d Omega=("area")/(("radius")^(2))=(DeltaA)/(r^(2))`
Maximum value of solid angle is `4pi`
Angle subtended on `1 m^(2)` area on sphere of 1 m radius is called 1 steradian. Its symbol is Sr.
If `DeltaA=1m^(2) and r=1 m "then" Omega=1` Sr