A solid spherical ball of radius $\frac{5}{9} \mathrm{m}$ is connected to a point $\mathrm{A}$ on the wall with the help of a string which makes an angle $\theta =45°$ with the vertical. The sphere can rotate freely about its central axis and it is set into rotational motion against the vertical face of the wall with an angular velocity $100 \mathrm{rad} {\mathrm{s}}^{-1}$. In how much time (in $\mathrm{s}$) will it come to rest? [$\mathrm{\mu }=0.1$]