Two equal masses m are attached by a string. One mass lies at radial distance r from the center of a horizontal turntable which rotates with constant angular velocity $\omega$ , while the second hangs from the strings inside the turntable’s hollow spindle (see figure). The coefficient of static friction between the turntable and the mass lying on it is  ${\mu }_s=0.5$. The maximum and minimum values of r such that the mass lying on the turntable does not slide are  $r_{\max },r_{\min }$. Find the ratio $r_{\max }/r_{\min }$ .