$11\mathrm{.}7($AIB$).$ A solid shaft carrying a flywheel of mass $100$ kg and radius of gyration $0\mathrm{.}4$m rotates at a uniform

speed of $75$ revimin. During service, a bearing $3$ m from the flywheel suddenly seizesproducinga fixation of the shaft

at this point. Neglecting the inertia of the shaft itself determine the necessary shaft diameter if the instantaneous

shear stress produced in the shaft does not exceed $180$ MN$/$mZ$.$ For the shaft material G $=80$ GN$/$m$2.$ Assume all

kinetic energy of the shaft is taken up as strain energy without any losses.