A particle is moving in a circle of radius \( 50 \, \text{cm} \) in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at \( t = 0 \) is \( 4 \, \text{m/s} \), the time taken to complete the first revolution will be \( \dfrac{1}{\alpha} \big[ 1 - e^{-2\pi} \big] \, \text{s} \). where \( \alpha = \) __________.
