The bottom surface of a disk is partially in touch with a layer of oil $($dynamic viscosity is $0\mathrm{.}35Pa.s)$ with thickness $t=1\mathrm{.}5mm,$ as shows in the figure. Four sensors are attached to the upper surface of the disk. Sensors will be detached from the disk if sensor has velocity $($V$\_$sensor$)$ greater then $25\mathrm{.}2\frac{m}{s}.$ Given that outer radius R$\_2$ of the disk is $0\mathrm{.}2m,$ calculate the value of inner radius R$\_1($in meter$)$ such that the disk can be rotate by torque of $50N.$m with maximum allowable velocity.