Mechanical Properties of Solids Chapter-Wise Test 11

Correct answer Carries: 4.

Wrong Answer Carries: -1.

An aluminium wire of length \( 1.7 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.34 \, \text{mm} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the force applied?

Young's modulus: \( Y = \frac{F L}{A \Delta L} \).

Rearrange: \( F = \frac{Y A \Delta L}{L} \).

Substitute: \( \Delta L = 0.34 \times 10^{-3} \, \text{m} \).

\( F = \frac{7 \times 10^{10} \times 2 \times 10^{-6} \times 0.34 \times 10^{-3}}{1.7} = \frac{47.6}{1.7} \approx 28 \, \text{N} \).

\( 25 \, \text{N} \)
\( 30 \, \text{N} \)
\( 20 \, \text{N} \)
\( 28 \, \text{N} \)
4

A glass slab of volume \( 0.04 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 7 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the fractional change in volume?

Bulk modulus: \( B = -\frac{p}{\frac{\Delta V}{V}} \).

Rearrange: \( \frac{\Delta V}{V} = -\frac{p}{B} = -\frac{7 \times 10^6}{3.7 \times 10^{10}} \approx -1.89 \times 10^{-4} \).

Magnitude: \( 1.89 \times 10^{-4} \).

\( 1.89 \times 10^{-4} \)
\( 2 \times 10^{-4} \)
\( 1.5 \times 10^{-4} \)
\( 1 \times 10^{-4} \)
1

An aluminium wire of length \( 1.5 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 140 \, \text{N} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the elongation?

Young's modulus: \( Y = \frac{F L}{A \Delta L} \).

Rearrange: \( \Delta L = \frac{F L}{A Y} \).

Substitute: \( \Delta L = \frac{140 \times 1.5}{2 \times 10^{-6} \times 7 \times 10^{10}} = \frac{210}{1.4 \times 10^5} = 1.5 \times 10^{-3} \, \text{m} = 1.5 \, \text{mm} \).

\( 1 \, \text{mm} \)
\( 2 \, \text{mm} \)
\( 1.5 \, \text{mm} \)
\( 3 \, \text{mm} \)
3

A steel rod of length 0.6 m and cross-sectional area 5 × 10-6 m2 is compressed by a force producing a strain of 3 × 10-4. If the Young's modulus of steel is 2 × 1011 N/m2, what is the force applied?

Young's modulus: Y = Stress / Strain.

Stress: Stress = Y × Strain = 2 × 1011 × 3 × 10-4 = 6 × 107 N/m2.

Force: F = Stress × A = 6 × 107 × 5 × 10-6 = 300 N.

200 N
400 N
300 N
500 N
3

A copper wire of length 1.2 m and cross-sectional area 1.5 × 10-6 m2 is stretched by a force producing a stress of 2 × 107 N/m2. If the Young's modulus of copper is 1.1 × 1011 N/m2, what is the strain?

Young's modulus: Y = Stress / Strain.

Strain: Strain = Stress / Y = (2 × 107) / (1.1 × 1011) ≈ 1.82 × 10-4.

1 × 10-4
2 × 10-4
1.82 × 10-4
1.5 × 10-4
3

A copper wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 1 \times 10^{-4} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the force applied?

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

Stress: \( \text{Stress} = Y \times \text{Strain} = 1.1 \times 10^{11} \times 1 \times 10^{-4} = 1.1 \times 10^7 \, \text{N/m}^2 \).

Force: \( F = \text{Stress} \times A = 1.1 \times 10^7 \times 2 \times 10^{-6} = 22 \, \text{N} \).

\( 20 \, \text{N} \)
\( 22 \, \text{N} \)
\( 25 \, \text{N} \)
\( 30 \, \text{N} \)
2

A brass wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 5 \times 10^{-4} \). 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: \( \text{Stress} = Y \times \text{Strain} = 9 \times 10^{10} \times 5 \times 10^{-4} = 4.5 \times 10^7 \, \text{N/m}^2 \).

Force: \( F = \text{Stress} \times A = 4.5 \times 10^7 \times 3 \times 10^{-6} = 135 \, \text{N} \).

\( 100 \, \text{N} \)
\( 150 \, \text{N} \)
\( 135 \, \text{N} \)
\( 120 \, \text{N} \)
3

What characterizes the stress-strain behavior of a material in the region where plastic deformation begins?

When plastic deformation begins, the material experiences permanent deformation, meaning it does not return to its original shape even after the load is removed.

The material obeys Hooke’s law
The material experiences permanent deformation
The material fractures immediately
The material undergoes purely elastic deformation
2

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

In the stress-strain behavior of a ductile material, what happens after the maximum stress the material can endure?

After the maximum stress (ultimate tensile strength), a ductile material experiences a decrease in stress with additional strain, leading to eventual fracture.

The material begins to fracture
The material returns to its original shape
The proportionality between stress and strain holds
The material undergoes elastic deformation only
1

Performance Summary

Score:

Category Details
Total Attempts:
Total Skipped:
Total Wrong Answers:
Total Correct Answers:
Time Taken:
Average Time Taken per Question:
Accuracy:
0