A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $\mathrm { t } = 0$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the time taken to complete the first revolution will be $\frac { 1 } { \alpha } \left[ 1 - \mathrm { e } ^ { - 2 \pi } \right] \mathrm { s }$, where $\alpha =$ $\_\_\_\_$ .