A thin circular coin of mass \( 5 \, \text{gm} \) and radius \( \dfrac{4}{3} \, \text{cm} \) is initially in a horizontal xy-plane. The coin is tossed vertically up (\( +z \) direction) by applying an impulse of \( \sqrt{\dfrac{\pi}{2}} \times 10^{-2} \, \text{N- s} \) at a distance \( \dfrac{2}{3} \, \text{cm} \) from its centre. The coin spins about its diameter and moves along the \( +z \) direction. By the time the coin reaches back to its initial position, it completes \( n \) rotations. The value of \( n \) is ________.
[Given the acceleration due to gravity \( g = 10 \, \text{m s}^{-2} \)]
