1. A helical idler gear (see Chapter 15) is to be supported at the center of a short hollow circular shaft using a single-row radial ball bearing. The inner race is presses on the fixed nonrotating shaft, and the rotating gear is attached to the outer race of the bearing. The gear is to rotate at 900 rpm. The forces in the gear produce a resultant radial force on the bearing of 1800 N and a resultant thrust force on the bearing if 1460 N. The assembly is subjected to light shock loading conditions. Based on preliminary stress analysis of the shaft, it must have at least a 50-mm outside diameter. It is desired to use a bearing that will have a life of 3000 hours with 99 percent reliability. Select the smallest acceptable bearing (bore) .