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GATE 2016 ME (ME1) – Question 18

Mechanics of Materials · Torsion of circular shafts · 1 mark · Multiple choice

Two hollow bars of the same material have concentric circular cross sections as shown, with $r_3>r_1$, $r_4>r_2$ and equal cross-sectional areas. Their torsional rigidities are $J_1,J_2$ for left and right bars. The ratio $J_2/J_1$ is ______.

Diagram for GATE 2016 ME (ME1) question 18
  1. > 1
  2. < 0.5
  3. =1
  4. between 0.5 and 1

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Show answer and explanation

Correct answer: (A) > 1

Explanation

For an annulus, polar second moment is J=π(ro⁴−ri⁴)/2=(A/2)(ro²+ri²). Both bars have equal area and the same shear modulus, while both radii of the second are larger. Its sum of squared radii is therefore larger, giving **J2/J1>1, A**. Moving material outward improves torsional rigidity.