Agear of inner and outer radii 25 mm and 125 mm, respectively is shrunk onto a hollow shaft of outer radius 25.05 mm. both members are made of steel with e = 200 gpa, v = 1/3, and rho = 7.8 kn. s^2/m^4. if the assembly is to rotate, calculate

(a) the speed in rpm at which the interface pressure becomes zero, and
(b) the maximum stress at this speed. you may neglect the radial displacement of the shaft.