Mechanical Properties of Solids

Q. A beam of length 4 m and uniform cross-section is subjected to a bending moment of 200 Nm. If the moment of inertia of the beam's cross-section is 1e-6 m⁴, what is the maximum bending stress?

A. 50 MPa
B. 100 MPa
C. 150 MPa
D. 200 MPa

Solution

Maximum bending stress = (M * c) / I = (200 Nm * 0.2 m) / (1e-6 m⁴) = 100 MPa.

Correct Answer: B — 100 MPa

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Q. A cylindrical rod of diameter 20 mm and length 1 m is subjected to a compressive load of 100 kN. Calculate the compressive stress in the rod.

A. 10 MPa
B. 20 MPa
C. 30 MPa
D. 40 MPa

Solution

Compressive stress = Force / Area = 100,000 N / (π * (0.01 m)²) = 10 MPa.

Correct Answer: A — 10 MPa

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Q. A material has a Poisson's ratio of 0.3. If it is stretched in one direction, what is the ratio of lateral strain to longitudinal strain?

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Solution

The ratio of lateral strain to longitudinal strain is equal to the Poisson's ratio, which is 0.3.

Correct Answer: C — 0.3

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Q. A material has a yield strength of 250 MPa and a tensile strength of 400 MPa. What is the percentage elongation at fracture if the material is ductile?

A. 5%
B. 10%
C. 15%
D. 20%

Solution

For ductile materials, percentage elongation at fracture can be around 20%.

Correct Answer: D — 20%

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Q. A steel rod of length 2 m and cross-sectional area 10 mm² is subjected to a tensile force of 50 kN. What is the elongation of the rod? (Young's modulus of steel = 200 GPa)

A. 0.005 m
B. 0.01 m
C. 0.015 m
D. 0.02 m

Solution

Elongation (ΔL) = (Force * Length) / (Area * Young's modulus) = (50,000 N * 2 m) / (10e-6 m² * 200e9 Pa) = 0.005 m.

Correct Answer: A — 0.005 m

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Q. A wire of length 3 m and diameter 2 mm is stretched by a load of 100 N. Calculate the tensile strain if the Young's modulus of the wire is 200 GPa.

A. 0.001
B. 0.002
C. 0.003
D. 0.004

Solution

Tensile strain = Stress / Young's modulus = (100 N / (π * (0.001 m)²)) / (200e9 Pa) = 0.002.

Correct Answer: B — 0.002

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Q. If a material has a tensile strength of 600 MPa and a yield strength of 300 MPa, what is the factor of safety if the working load is 150 MPa?

A. 1.5
B. 2
C. 2.5
D. 3

Solution

Factor of safety = Yield strength / Working load = 300 MPa / 150 MPa = 2.

Correct Answer: B — 2

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Q. If the shear modulus of a material is 80 GPa, what is the modulus of resilience if the yield strength is 400 MPa?

A. 0.5 J/m³
B. 1 J/m³
C. 2 J/m³
D. 4 J/m³

Solution

Modulus of resilience = (Yield strength²) / (2 * Shear modulus) = (400 MPa)² / (2 * 80 GPa) = 2 J/m³.

Correct Answer: C — 2 J/m³

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Q. What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.02 m³ for a volume of 1 m³?

A. 200 MPa
B. 250 MPa
C. 300 MPa
D. 350 MPa

Solution

Bulk modulus (K) = -ΔP / (ΔV/V) = -50 MPa / (-0.02 m³ / 1 m³) = 250 MPa.

Correct Answer: B — 250 MPa

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Q. What is the Young's modulus of a material if a tensile stress of 200 MPa produces a tensile strain of 0.002?

A. 100 GPa
B. 200 GPa
C. 300 GPa
D. 400 GPa

Solution

Young's modulus (E) = Stress / Strain = 200 MPa / 0.002 = 100 GPa.

Correct Answer: B — 200 GPa

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Mechanical Properties of Solids

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