Strength of Material MCQ Set 8

STRENGTH OF MATERIAL MCQ SET 8

Q1. The moment of inertia of a rectangle about its base is:

A) bh³/12
B) bh³/3
C) bh³/36
D) bh³/24

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Answer: B) bh³/3
Explanation: For base axis, I = (b*h³)/3.

Q2. The centroid of a semicircle lies at a distance from the base equal to:

A) 4r/3π
B) r/2
C) 2r/π
D) 3r/4

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Answer: A) 4r/3π
Explanation: The centroid of a semicircle from its base = 4r/(3π).

Q3. The Euler’s formula for a column with both ends pinned is:

A) π²EI/L²
B) π²EI/2L²
C) 4π²EI/L²
D) π²EI/4L²

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Answer: A) π²EI/L²
Explanation: Critical load for both ends pinned = π²EI/L².

Q4. Slenderness ratio is defined as:

A) L/r
B) r/L
C) L/d
D) d/L

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Answer: A) L/r
Explanation: Slenderness ratio = Effective length / Radius of gyration.

Q5. A short column fails due to:

A) Buckling
B) Crushing
C) Shear
D) Fatigue

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Answer: B) Crushing
Explanation: Short columns fail by direct compression or crushing, not by buckling.

Q6. A long column generally fails due to:

A) Buckling
B) Crushing
C) Shear
D) Torsion

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Answer: A) Buckling
Explanation: Long columns fail by lateral deflection or buckling before the material yields.

Q7. Euler’s formula is applicable only for:

A) Short columns
B) Long slender columns
C) All columns
D) Intermediate columns

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Answer: B) Long slender columns
Explanation: Euler’s theory assumes the column is perfectly elastic and long.

Q8. Effective length of a column with both ends fixed is:

A) L
B) L/2
C) L/√2
D) 2L

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Answer: B) L/2
Explanation: For both ends fixed, effective length = 0.5 × actual length.

Q9. In a column, radius of gyration is given by:

A) I/A
B) √(I/A)
C) A/I
D) L/I

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Answer: B) √(I/A)
Explanation: Radius of gyration relates area and moment of inertia by r= √I/A

Q10. The critical load for a column with one end fixed and other free is:

A) π²EI/L²
B) π²EI/4L²
C) π²EI/2L²
D) π²EI/16L²

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 Answer: D) π²EI/16L²
Explanation: Effective length = 2L, hence Pcr = π²EI/(2L)² = π²EI/4L² × 1/4 = π²EI/16L².