$2-)(60$ points$)$ A shaft is supported by two bearings placed $1$ m apart. A $600$ mm diameter pulley is mounted at a distance of $300$ mm to the right of left hand bearing and this drives a pulley directly below it with the help of belt having maximum tension of $2\mathrm{.}25$ kN $.$ Another pulley $400$ mm diameter is placed $200$ mm to the left of right hand bearing and is driven with the help of electric motor and belt, which is placed horizontally to the right. The angle of contact for both the pulleys is $180$ and $=0\mathrm{.}24.$ Determine the suitable diameter for a solid shaft, allowing working stress of $63$ MPa in tension and $42$ MPa in shear for the material of shaft. Assume that the torque on one pulley is equal to that on the other pulley.