STRENGTH OF MATERIAL MCQ SET 8
Q1. The moment of inertia of a rectangle about its base is:
A) bhยณ/12
B) bhยณ/3
C) bhยณ/36
D) bhยณ/24
Answer: B) bhยณ/3
Explanation: For base axis, I = (b*hยณ)/3.
Q2. The centroid of a semicircle lies at a distance from the base equal to:
A) 4r/3ฯ
B) r/2
C) 2r/ฯ
D) 3r/4
Answer: A) 4r/3ฯ
Explanation: The centroid of a semicircle from its base = 4r/(3ฯ).
Q3. The Eulerโs formula for a column with both ends pinned is:
A) ฯยฒEI/Lยฒ
B) ฯยฒEI/2Lยฒ
C) 4ฯยฒEI/Lยฒ
D) ฯยฒEI/4Lยฒ
Answer: A) ฯยฒEI/Lยฒ
Explanation: Critical load for both ends pinned = ฯยฒEI/Lยฒ.
Q4. Slenderness ratio is defined as:
A) L/r
B) r/L
C) L/d
D) d/L
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
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
Answer: A) Buckling
Explanation: Long columns fail by lateral deflection or buckling before the material yields.
Q7. Eulerโs formula is applicable only for:
A) Short columns
B) Long slender columns
C) All columns
D) Intermediate columns
Answer: B) Long slender columns
Explanation: Eulerโs 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/โ2
D) 2L
Answer: B) L/2
Explanation: For both ends fixed, effective length = 0.5 ร actual length.
Q9. In a column, radius of gyration is given by:
A) I/A
B) โ(I/A)
C) A/I
D) L/I
Answer: B) โ(I/A)
Explanation: Radius of gyration relates area and moment of inertia by r= โI/A
Q10. The critical load for a column with one end fixed and other free is:
A) ฯยฒEI/Lยฒ
B) ฯยฒEI/4Lยฒ
C) ฯยฒEI/2Lยฒ
D) ฯยฒEI/16Lยฒ
ย Answer: D) ฯยฒEI/16Lยฒ
Explanation: Effective length = 2L, hence Pcr = ฯยฒEI/(2L)ยฒ = ฯยฒEI/4Lยฒ ร 1/4 = ฯยฒEI/16Lยฒ.
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