Mechanical Properties of Solids Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A brass block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 6 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Shear modulus: \( G = \frac{F / A}{\Delta x / L} \).

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

Area: \( A = 0.5 \times 0.3 = 0.15 \, \text{m}^2 \), \( L = 0.2 \, \text{m} \).

Substitute: \( \Delta x = \frac{6 \times 10^4 \times 0.2}{0.15 \times 3.6 \times 10^{10}} = \frac{12000}{5.4 \times 10^9} \approx 2.22 \times 10^{-6} \, \text{m} \).

\( 2 \times 10^{-6} \, \text{m} \)
\( 2.22 \times 10^{-6} \, \text{m} \)
\( 2.5 \times 10^{-6} \, \text{m} \)
\( 1.5 \times 10^{-6} \, \text{m} \)
2

A steel wire of length \( 2.7 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 450 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Stress: \( \text{Stress} = \frac{F}{A} = \frac{450}{3 \times 10^{-6}} = 1.5 \times 10^8 \, \text{N/m}^2 \).

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

Strain: \( \text{Strain} = \frac{\text{Stress}}{Y} = \frac{1.5 \times 10^8}{2 \times 10^{11}} = 7.5 \times 10^{-4} \).

\( 7 \times 10^{-4} \)
\( 7.5 \times 10^{-4} \)
\( 8 \times 10^{-4} \)
\( 6 \times 10^{-4} \)
2

A steel wire of length 5 m and cross-sectional area 4 × 10-6 m2 is stretched by 0.5 mm. If the Young's modulus of steel is 2 × 1011 N/m2, what is the stress?

Young's modulus: Y = (Stress) / (Strain).

Strain: Strain = ΔL / L = (0.5 × 10-3) / 5 = 1 × 10-4.

Stress: Stress = Y × Strain = 2 × 1011 × 1 × 10-4 = 2 × 107 N/m2.

1 × 107 N/m2
3 × 107 N/m2
2 × 107 N/m2
4 × 107 N/m2
3

A copper block of dimensions \( 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 7 \times 10^4 \, \text{N} \). If the shear modulus of copper is \( 4.2 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

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

Shear stress: \( \text{Shear stress} = \frac{F}{A} \), \( A = 0.6 \times 0.4 = 0.24 \, \text{m}^2 \).

Shear stress: \( \frac{7 \times 10^4}{0.24} \approx 2.92 \times 10^5 \, \text{N/m}^2 \).

Shear strain: \( \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{2.92 \times 10^5}{4.2 \times 10^{10}} \approx 6.95 \times 10^{-6} \).

\( 6.95 \times 10^{-6} \)
\( 7 \times 10^{-6} \)
\( 6 \times 10^{-6} \)
\( 5 \times 10^{-6} \)
1

What is the key difference between elastic and plastic deformation in a material?

Elastic deformation is reversible, meaning the material returns to its original shape after the load is removed, while plastic deformation results in permanent changes.

Elastic deformation occurs only in solids
Plastic deformation occurs at lower stress
Elastic deformation involves higher energy
Elastic deformation is reversible, plastic is not
4

An aluminium rod of length \( 1.4 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is compressed by a force producing a stress of \( 3 \times 10^7 \, \text{N/m}^2 \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the compression?

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

Strain: \( \text{Strain} = \frac{\text{Stress}}{Y} = \frac{3 \times 10^7}{7 \times 10^{10}} \approx 4.29 \times 10^{-4} \).

Compression: \( \Delta L = \text{Strain} \times L = 4.29 \times 10^{-4} \times 1.4 \approx 6 \times 10^{-4} \, \text{m} = 0.6 \, \text{mm} \).

\( 0.5 \, \text{mm} \)
\( 0.7 \, \text{mm} \)
\( 0.4 \, \text{mm} \)
\( 0.6 \, \text{mm} \)
4

A glass slab experiences a hydraulic pressure of 8 × 106 N/m2. If the bulk modulus of glass is 3.7 × 1010 N/m2, what is the fractional change in volume?

Bulk modulus: B = -p / (ΔV / V).

Rearrange: ΔV / V = -p / B.

Substitute: ΔV / V = -(8 × 106) / (3.7 × 1010) ≈ -2.16 × 10-4.

Magnitude: 2.16 × 10-4.

2 × 10-4
2.5 × 10-4
2.16 × 10-4
3 × 10-4
3

A steel wire of length 2 m and cross-sectional area 2 × 10-6 m2 is stretched by a force of 200 N. If the Young's modulus of steel is 2 × 1011 N/m2, what is the elongation of the wire?

Using Young's modulus formula: Y = (F L) / (A ΔL).

Rearrange for elongation: ΔL = (F L) / (A Y).

Substitute values: ΔL = (200 × 2) / (2 × 10-6 × 2 × 1011).

Calculate: ΔL = 400 / (4 × 105) = 10-3 m = 1 mm.

1 mm
2 mm
0.5 mm
1.5 mm
1

Which modulus describes a material’s resistance to volume change under uniform pressure in all directions?

The bulk modulus measures a material’s resistance to volume change when subjected to uniform pressure (hydraulic stress) in all directions, affecting volume but not shape.

Young’s modulus
Shear modulus
Bulk modulus
Elastic modulus
3

A steel cable of radius 0.02 m is used to lift a load. If the maximum stress it can withstand is 1 × 108 N/m2, what is the maximum load it can support? (Take π ≈ 3.14)

Stress: Stress = F / A.

Area: A = π r2 = 3.14 × (0.02)2 = 3.14 × 0.0004 = 1.256 × 10-3 m2.

Maximum force: F = Stress × A = 1 × 108 × 1.256 × 10-3 = 1.256 × 105 N.

1 × 105 N
1.256 × 105 N
1.5 × 105 N
2 × 105 N
2

Performance Summary

Score:

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