This is a problem exploring the role of lubrication surface geometry and speed in causing a frictional force. A metal disk of density, collar, of axial length, L, and radius, R2, has a hole drilled through the center in the axial direction. The hole is of radius, R1. A rod of length much greater than L and radius R1 is slipped through the hole. The pre-factor is a fraction denoting how much smaller the rod radius is with respect to the hole radius. The rod is lubricated with a fluid of viscosity and density, . This lubricating fluid takes up the entirety of the space between the rod and the hole wall of the collar. You may assume it is both Newtonian and incompressible. Air is surrounding the rod and collar. You conduct an experiment that involves orienting the rod and collar vertically and pulling the rod upward, letting go of the collar at the same time. What is the velocity of the rod in order to keep the collar in the same position? Simplify this expression by assuming that R2 is much bigger than R1 and that collar is much bigger than . Using a equal to 0.99, calculate the velocity for water, 10W30 oil and honey as the lubricating fluid. You may assume that the collar is made of a material of density 8000 kg/m3 and the outer radius of the disk is 5 cm.