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GATE 2016 ME (ME1) – Question 19

Mechanics of Materials · Deflection of beams · 1 mark · Multiple choice

A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased by 19%, the tip deflection decreases approximately by

  1. 19%
  2. 29%
  3. 41%
  4. 50%

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Show answer and explanation

Correct answer: (D) 50%

Explanation

For fixed load, length and material, deflection is inversely proportional to I. A square section has I=a⁴/12, so increasing a by19% gives δnew/δold=1/(1.19)⁴≈0.499. The decrease is about50.1%, matching **50%, D**.