Properties of Matter - Mechanical Properties of Solids

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Q1. A wire of length L and diameter d is stretched by a force F. If the diameter is halved while keeping the length constant, what happens to the stress in the wire? (2022)

Solution:

Stress (σ) = Force (F) / Area (A). Halving the diameter increases the area by a factor of 4, thus stress quadruples.

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Q2. Which of the following describes the behavior of a ductile material? (2023)

Solution:

Ductile materials can be stretched into wires without breaking.

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Q3. Which of the following is a characteristic of elastic materials? (2023)

Solution:

Elastic materials return to their original shape after the removal of the applied force.

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Q4. A material has a Poisson's ratio of 0.3. If it is stretched in one direction, what is the expected lateral contraction ratio? (2019)

Solution:

Poisson's ratio (ν) = - (lateral strain) / (longitudinal strain), thus the lateral contraction ratio is 0.3.

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Q5. What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)

Solution:

Bulk modulus (K) = -ΔP / (ΔV/V) = -50 MPa / (-0.002 m³ / 1 m³) = 25000 MPa = 25 GPa.

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Q6. If a material has a shear modulus of 80 GPa and a shear stress of 40 MPa is applied, what is the shear strain? (2023)

Solution:

Shear strain (γ) = Shear stress (τ) / Shear modulus (G) = 40 MPa / 80 GPa = 0.0005.

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Q7. What is the Young's modulus of a material if a stress of 200 MPa produces a strain of 0.01? (2021)

Solution:

Young's modulus (E) = Stress / Strain = 200 MPa / 0.01 = 20000 MPa = 2000 MPa.

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Q8. What happens to the volume of a material when it is subjected to uniform pressure? (2019)

Solution:

Uniform pressure typically causes a decrease in volume, known as compression.

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Q9. What is the Poisson's ratio for a material if a longitudinal strain of 0.02 results in a lateral strain of 0.008? (2022)

Solution:

Poisson's ratio (ν) = -lateral strain / longitudinal strain = -0.008 / 0.02 = 0.4.

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Q10. What is the primary reason for the brittleness of certain materials? (2023)

Solution:

Brittleness is primarily due to high atomic bonding energy, which prevents the material from deforming plastically.

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