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 it's acceleration are…

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