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GATE 2016 ME (ME2) – Question 42

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

A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figure. Vertical forces of magnitude P are applied at the two ends as shown in the figure. The shear modulus for the cylinder is G and the Young’s modulus is E. The vertical deflection at point A is

Diagram for GATE 2016 ME (ME2) question 42
  1. $PL^3/(\pi R^4G)$
  2. $PL^3/(\pi R^4E)$
  3. $2PL^3/(\pi R^4E)$
  4. $4PL^3/(\pi R^4G)$

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Correct answer: (D) $4PL^3/(\pi R^4G)$

Explanation

The equal opposite end forces produce torque2PL on the cylinder without net transverse force. Cylinder length is L and polar moment J=πR⁴/2, so twist is(2PL)L/(GJ)=4PL²/(πGR⁴). The rigid arm endpoint displacement is L times this small angle: **4PL³/(πGR⁴), D**.