A vertical shaft of 0.5 cm diameter is 20 cm long and is supported in long bearings at its ends. A disc weighing 50 kgf is attached at the centre of the shaft, Neglecting any increase in stiffness due to the attachment of the disc to the shaft, find the critical speed of rotation and the maximum bending stress when the shaft is rotating at 75% of the critical speed. The centre of the disc is 0.25 mm from the geometric axis of the shaft. E = 20 × 105 kgf/cm2.