Physics · Units And Measurements · NEET
Neither in the old sense. NCERT lists seven base units (metre, kilogram, second, ampere, kelvin, mole, candela) and then names two more units defined separately: radian for plane angle and steradian for solid angle. These two are called supplementary units. So for NEET, remember: radian and steradian are NOT among the seven base units and are NOT ordinary derived units — they are the two supplementary SI units.
A radian is defined as arc length divided by radius: angle = ds/r. Both arc and radius are lengths (metres), so metre / metre = 1, no dimension left. A steradian is area on a sphere divided by radius squared: angle = dA/r squared. Here metre squared / metre squared = 1, again dimensionless. NCERT states clearly that both these are dimensionless quantities. That is why in dimensional analysis an angle counts as a pure number.
A full circle has an arc length equal to the whole circumference, 2*pi*r. So the plane angle = (2*pi*r)/r = 2*pi radian. A full sphere has surface area 4*pi*r squared, so the solid angle = (4*pi*r squared)/(r squared) = 4*pi steradian. Quick numbers to remember: full circle = 2*pi rad (about 6.28), full sphere = 4*pi sr (about 12.57).
A radian measures a flat (2D) angle, like the opening of a slice of pizza seen from the side. A steradian measures a solid (3D) angle, like the cone of the whole pizza slice or the spread of a torch beam. Radian uses arc / radius (one power of r); steradian uses area / radius squared (two powers of r). One flat angle, one 3D cone-shaped angle.
Because a unit is a chosen standard for reporting a number, and dimensionless does not mean unit-less in practice. We still need to say whether 1.57 means radians or degrees, and whether a solid angle is in steradians. Radian and steradian give a clear, agreed way to state angles. In dimensional formulas they act as 1 (pure number), but as reporting units they matter.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The radian (symbol rad) for plane angle and the steradian (symbol sr) for solid angle. These are added on top of the seven base units.
No. 1 radian is about 57.3 degrees. A full circle is 2*pi radian = 360 degrees, so 1 rad = 180/pi degrees, which is roughly 57.3 degrees.
Both have dimensional formula [M^0 L^0 T^0], that is dimension 1 (dimensionless), because radian = length/length and steradian = area/area.
A steradian is the solid angle dOmega equal to the intercepted area dA on a sphere divided by the square of the radius: dOmega = dA / r squared, with the apex at the centre of the sphere.
NEET Units and Measurements questions often ask which units are supplementary and whether angle has a dimension. Knowing radian and steradian are supplementary and dimensionless saves you in both direct-recall and dimensional-consistency problems.
