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GATE CE — free MCQ practice

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GATE CE subjects

Civil Engineering (44)

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GATE Civil — Core TopicsStrength of Materials

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Centroid of a triangle lies at:Read the answer and worked solution →For equilibrium of a rigid body in 2D, the conditions are:Read the answer and worked solution →Moment of inertia of a rectangle (base b, height h) about its centroidal axis parallel to base is:Read the answer and worked solution →Young's modulus of steel is approximately:Read the answer and worked solution →

Worked practice questions

Centroid of a triangle lies at:

  1. Intersection of medians, at 1/3 height from base
  2. Random
  3. Midpoint of base
  4. Top vertex
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Correct answer: A. Intersection of medians, at 1/3 height from base

**Centroid:** intersection of three medians (line from vertex to opposite side's midpoint). Divides each median in 2:1 ratio (closer to side). Located at h/3 above the base for any triangle. For uniform-density triangle, centroid = center of mass.

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For equilibrium of a rigid body in 2D, the conditions are:

  1. Just moment
  2. ΣF≠0
  3. ΣF = 0
  4. ΣFx = 0, ΣFy = 0, and ΣM = 0 (3 equations)
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Correct answer: D. ΣFx = 0, ΣFy = 0, and ΣM = 0 (3 equations)

Static equilibrium in 2D: 3 independent equations — sum of forces in x = 0, sum of forces in y = 0, sum of moments about any point = 0. Allows solving structures with up to 3 unknown reactions (statically determinate).

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Moment of inertia of a rectangle (base b, height h) about its centroidal axis parallel to base is:

  1. b²h/12
  2. bh³/12
  3. bh²/6
  4. bh³/12
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Correct answer: B. bh³/12

I_xx = bh³/12 for rectangle about centroidal axis parallel to base. **About base:** bh³/3 (parallel axis: I = I_c + Ad², so bh³/12 + bh × (h/2)² = bh³/12 + bh³/4 = bh³/3).

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