The toy-top (initially at rest) shown in the figure, has a moment of inertia $4\times {10}^{-4} \mathrm{kg} {\mathrm{m}}^2$ and it is free to rotate about the stationary axis $AA\text{'}$. The string wrapped around the peg of the toy-top is pulled outwards without letting it slip and simultaneously maintaining a constant tension of $5.625 \mathrm{N}$. If $\omega$ is the angular speed (in $\mathrm{rad} {\mathrm{s}}^{-1}$) of the top after $80 \mathrm{cm}$ of string has been pulled off the peg, then mark your answer as $\frac{\omega }{100}$.