A rod of 20 mm dia is fixed to the ceiling of a roof on one end. A rotor of 50 kg mass is attached to the free end with bearings. The CG of the rotor is 10 mm away from the shaft axis. The rotor is rotating at 600 rpm. The max tensile stress (in N/Sq. mm) in the rod is nearly equal to
- A. \pi/2
- B. 200 \pi
- C. 300 \pi
- D. 400 \pi
Answer: D. 400 \pi
Explanation: Centrifugal force F = m \omega² e. \omega = 2\pi(600)/60 = 20\pi. F = 50 * (20\pi)^2 * 0.01 = 200\pi² N. Moment M = F * L = 200\pi² * 0.5 = 100\pi² Nm = 100000\pi² Nmm. Z = \pi d³ / 32 = \pi (20)^3 / 32 = 250\pi. Stress = M/Z = 100000\pi² / 250\pi = 400\pi N/mm².