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GATE 2017 ME (ME1) – Question 26

Mechanics of Materials · Thin-walled pressure vessels · 1 mark · Multiple choice

A beam has a circular cross-section of diameter $d$. The ratio of its second moment of area about the neutral axis to its section modulus is

  1. $d/2$
  2. $\pi d/2$
  3. $d$
  4. $\pi d$

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Correct answer: (A) $d/2$

Explanation

Elastic section modulus is $Z=I/c$, where c is the distance from neutral axis to extreme fibre. Therefore $I/Z=c$. For the circular section, $c=d/2$, so the ratio is $d/2$, A. This avoids separately substituting the expressions for I and Z.

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