Mechanical Properties of Solids Chapter-Wise Test 12

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Which modulus is not applicable for describing the elastic behavior of liquids and gases under shear stress?

The shear modulus is not applicable for liquids and gases because they do not sustain shear stress and instead flow; only solids have a defined shear modulus.

Bulk modulus
Young’s modulus
Compressive modulus
Shear modulus
4

A brass wire of length 3 m and cross-sectional area 2 × 10-6 m2 is stretched by a force of 400 N. If the Young's modulus of brass is 9 × 1010 N/m2, what is the elongation?

Young's modulus: Y = (F L) / (A ΔL).

Rearrange: ΔL = (F L) / (A Y).

Substitute: ΔL = (400 × 3) / (2 × 10-6 × 9 × 1010) = 1200 / (1.8 × 105) = 6.67 × 10-3 m ≈ 6.67 mm.

6.67 mm
5 mm
8 mm
10 mm
1

A copper wire of length \( 2.5 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 200 \, \text{N} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the stress?

Stress: \( \text{Stress} = \frac{F}{A} = \frac{200}{2 \times 10^{-6}} = 1 \times 10^8 \, \text{N/m}^2 \).

\( 5 \times 10^7 \, \text{N/m}^2 \)
\( 1.5 \times 10^8 \, \text{N/m}^2 \)
\( 1 \times 10^8 \, \text{N/m}^2 \)
\( 2 \times 10^8 \, \text{N/m}^2 \)
3

A brass wire of length \( 1.9 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 2 \times 10^{-4} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the force applied?

Young's modulus: \( Y = \frac{\text{Stress}}{\text{Strain}} \).

Stress: \( \text{Stress} = Y \times \text{Strain} = 9 \times 10^{10} \times 2 \times 10^{-4} = 1.8 \times 10^7 \, \text{N/m}^2 \).

Force: \( F = \text{Stress} \times A = 1.8 \times 10^7 \times 2 \times 10^{-6} = 36 \, \text{N} \).

\( 30 \, \text{N} \)
\( 36 \, \text{N} \)
\( 40 \, \text{N} \)
\( 45 \, \text{N} \)
2

A steel block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 5 \times 10^4 \, \text{N} \). If the shear modulus of steel is \( 8.4 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Shear modulus: \( G = \frac{\text{Shear stress}}{\text{Shear strain}} \).

Shear stress: \( \text{Shear stress} = \frac{F}{A} \), \( A = 0.5 \times 0.3 = 0.15 \, \text{m}^2 \).

Shear stress: \( \frac{5 \times 10^4}{0.15} \approx 3.33 \times 10^5 \, \text{N/m}^2 \).

Shear strain: \( \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{3.33 \times 10^5}{8.4 \times 10^{10}} \approx 3.96 \times 10^{-6} \).

\( 3.5 \times 10^{-6} \)
\( 3.96 \times 10^{-6} \)
\( 4 \times 10^{-6} \)
\( 3 \times 10^{-6} \)
2

A brass wire of length \( 1.7 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 4 \times 10^{-4} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the stress?

Young's modulus: \( Y = \frac{\text{Stress}}{\text{Strain}} \).

Stress: \( \text{Stress} = Y \times \text{Strain} = 9 \times 10^{10} \times 4 \times 10^{-4} = 3.6 \times 10^7 \, \text{N/m}^2 \).

\( 3 \times 10^7 \, \text{N/m}^2 \)
\( 4 \times 10^7 \, \text{N/m}^2 \)
\( 3.6 \times 10^7 \, \text{N/m}^2 \)
\( 2.5 \times 10^7 \, \text{N/m}^2 \)
3

A brass plate experiences a shearing force of 4 × 104 N across an area of 0.05 m2. If the shear strain is 2 × 10-5, what is the shear modulus of brass?

Shear modulus: G = (Shear stress) / (Shear strain).

Shear stress: Shear stress = F / A = (4 × 104) / 0.05 = 8 × 105 N/m2.

Shear strain: 2 × 10-5.

Substitute: G = (8 × 105) / (2 × 10-5) = 4 × 1010 N/m2.

3 × 1010 N/m2
5 × 1010 N/m2
2 × 1010 N/m2
4 × 1010 N/m2
4

A steel wire of length \( 2.8 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.7 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Strain: \( \text{Strain} = \frac{\Delta L}{L} = \frac{0.7 \times 10^{-3}}{2.8} = 2.5 \times 10^{-4} \).

\( 2 \times 10^{-4} \)
\( 3 \times 10^{-4} \)
\( 1.5 \times 10^{-4} \)
\( 2.5 \times 10^{-4} \)
4

What distinguishes a ductile material from a brittle material in terms of stress-strain behavior?

A ductile material undergoes significant plastic deformation before fracture, allowing it to withstand larger strains, while a brittle material fractures with minimal plastic deformation.

Ductile materials have a larger shear modulus
Ductile materials undergo significant plastic deformation before fracture
Ductile materials break at a lower stress
Ductile materials have a lower bulk modulus
2

A brass rod of length 2 m and cross-sectional area 5 × 10-6 m2 is compressed by a force of 1000 N. If the Young's modulus of brass is 9 × 1010 N/m2, what is the longitudinal strain?

Stress: Stress = F / A = 1000 / (5 × 10-6) = 2 × 108 N/m2.

Young's modulus: Y = Stress / Strain.

Strain: Strain = Stress / Y = (2 × 108) / (9 × 1010) ≈ 2.22 × 10-3.

2 × 10-3
2.22 × 10-3
2.5 × 10-3
3 × 10-3
2

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