A conducting circular loop is rotated about its diameter at a constant angular speed of \(100 \, \text{rad s}^{-1}\) in a magnetic field of \(0.5 \, \text{T}\), perpendicular to the axis of rotation. When the loop is rotated by \(30^\circ\) from the horizontal position, the induced EMF is \(15.4 \, \text{mV}\). The radius of the loop is ______________ mm.
(Take \( \pi = \dfrac{22}{7} \))