A small bead of mass $108 \mathrm{~g}$ slides without friction along a semicircular wire of radius $10 \mathrm{~cm}$ that rotates about a vertical axis at a rate of $10 \sqrt{2} \mathrm{rad} \mathrm{s}^{-1}$ as shown in the figure. The value of $\theta$ for which the bead will remain stationary relative to the rotating wire is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$