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GATE 2016 ME (ME3) – Question 44

Mechanics of Materials · Torsion of circular shafts · 2 marks · Multiple choice

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, θS is the twist and τS is the maximum shear stress in the solid shaft, whereas θH is the twist and τH is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

  1. $\theta_S=\theta_H;\ \tau_S=\tau_H$
  2. $\theta_S>\theta_H;\ \tau_S>\tau_H$
  3. $\theta_S<\theta_H;\ \tau_S<\tau_H$
  4. $\theta_S=\theta_H;\ \tau_S<\tau_H$

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Correct answer: (D) $\theta_S=\theta_H;\ \tau_S<\tau_H$

Explanation

Twist is TL/(GJ), so equal T,L,G,J give equal twists. Maximum shear is Tr_outer/J. For equal J, the hollow shaft requires a larger outer radius than the solid shaft and therefore has greater maximum shear. This combination is **D**.