Elasticity
Q. In a material, if the strain is 0.01 and the Young's modulus is 200 GPa, what is the stress in the material?
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A.
2 MPa
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B.
20 MPa
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C.
200 MPa
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D.
2000 MPa
Solution
Stress = Young's modulus * strain = 200 GPa * 0.01 = 2 GPa = 2000 MPa.
Correct Answer: C — 200 MPa
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Q. In a shear stress-strain relationship, what does the slope of the linear portion represent?
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A.
Young's modulus
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B.
Shear modulus
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C.
Bulk modulus
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D.
Tensile strength
Solution
The slope of the linear portion of the shear stress-strain curve represents the shear modulus of the material.
Correct Answer: B — Shear modulus
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Q. In a tensile test, if a material exhibits a linear stress-strain relationship, what type of deformation is it undergoing?
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A.
Elastic deformation
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B.
Plastic deformation
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C.
Brittle fracture
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D.
Ductile fracture
Solution
A linear stress-strain relationship indicates that the material is undergoing elastic deformation.
Correct Answer: A — Elastic deformation
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Q. In a tensile test, if a material shows a linear relationship between stress and strain up to a certain point, this point is known as:
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A.
Yield point
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B.
Ultimate tensile strength
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C.
Elastic limit
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D.
Fracture point
Solution
The elastic limit is the maximum stress that a material can withstand while still returning to its original shape.
Correct Answer: C — Elastic limit
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Q. In a tensile test, if a material shows a linear relationship between stress and strain, it is said to be in which region?
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A.
Plastic region
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B.
Elastic region
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C.
Yield point
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D.
Fracture point
Solution
The linear relationship between stress and strain indicates that the material is in the elastic region.
Correct Answer: B — Elastic region
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Q. In a tensile test, if the stress-strain curve of a material shows a linear relationship, what does this indicate?
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A.
The material is elastic
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B.
The material is plastic
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C.
The material has failed
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D.
The material is brittle
Solution
A linear relationship in the stress-strain curve indicates that the material behaves elastically within that range.
Correct Answer: A — The material is elastic
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Q. In a tensile test, if the stress-strain curve shows a linear relationship, what does this indicate about the material?
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A.
It is inelastic
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B.
It is elastic
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C.
It has reached its yield point
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D.
It will break immediately
Solution
A linear relationship in the stress-strain curve indicates that the material behaves elastically within that range.
Correct Answer: B — It is elastic
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Q. In which of the following cases does a material exhibit plastic deformation?
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A.
When the stress is below the yield point
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B.
When the stress exceeds the yield point
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C.
When the material is unloaded
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D.
When the material is cooled
Solution
Plastic deformation occurs when the stress exceeds the yield point.
Correct Answer: B — When the stress exceeds the yield point
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Q. In which of the following scenarios does a material exhibit elastic behavior?
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A.
When it returns to its original shape after removing the load
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B.
When it permanently deforms
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C.
When it breaks
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D.
When it undergoes plastic deformation
Solution
A material exhibits elastic behavior when it returns to its original shape after the load is removed.
Correct Answer: A — When it returns to its original shape after removing the load
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Q. In which of the following scenarios does a material exhibit plastic deformation?
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A.
When the stress is below the yield point
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B.
When the stress exceeds the yield point
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C.
When the material is unloaded
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D.
When the material is cooled
Solution
Plastic deformation occurs when the stress exceeds the yield point of the material.
Correct Answer: B — When the stress exceeds the yield point
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Q. In which of the following scenarios does elastic deformation occur?
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A.
A rubber band being stretched
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B.
A metal rod being permanently bent
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C.
A glass breaking
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D.
A clay being molded
Solution
Elastic deformation occurs when the rubber band is stretched and returns to its original shape.
Correct Answer: A — A rubber band being stretched
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Q. The modulus of resilience is defined as:
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A.
The energy per unit volume stored in a material up to the yield point
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B.
The total energy absorbed by a material before fracture
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C.
The ratio of stress to strain
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D.
The maximum stress a material can withstand
Solution
The modulus of resilience is the energy per unit volume stored in a material up to the yield point.
Correct Answer: A — The energy per unit volume stored in a material up to the yield point
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Q. What happens to the Young's modulus of a material as temperature increases?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Becomes zero
Solution
Generally, the Young's modulus of materials decreases with an increase in temperature.
Correct Answer: B — Decreases
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Q. What happens to the Young's modulus of a material when it is heated?
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A.
It increases
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B.
It decreases
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C.
It remains constant
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D.
It becomes zero
Solution
Generally, the Young's modulus of a material decreases when it is heated due to increased atomic vibrations.
Correct Answer: B — It decreases
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Q. What is Poisson's ratio?
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A.
Lateral strain/Longitudinal strain
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B.
Longitudinal strain/Lateral strain
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C.
Stress/Strain
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D.
Strain/Stress
Solution
Poisson's ratio (ν) is defined as the ratio of lateral strain to longitudinal strain.
Correct Answer: A — Lateral strain/Longitudinal strain
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Q. What is the definition of Young's modulus?
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A.
The ratio of tensile stress to tensile strain
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B.
The ratio of compressive stress to compressive strain
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C.
The ratio of shear stress to shear strain
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D.
The ratio of bulk stress to bulk strain
Solution
Young's modulus is defined as the ratio of tensile stress to tensile strain, which measures the stiffness of a solid material.
Correct Answer: A — The ratio of tensile stress to tensile strain
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Q. What is the formula for the modulus of resilience?
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A.
U = 1/2 * σ * ε
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B.
U = σ * ε
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C.
U = 1/2 * ε^2
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D.
U = σ^2 / 2
Solution
The modulus of resilience is given by U = 1/2 * σ * ε, where σ is the yield stress and ε is the yield strain.
Correct Answer: A — U = 1/2 * σ * ε
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Q. What is the formula for Young's modulus?
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A.
Stress/Strain
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B.
Strain/Stress
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C.
Force/Area
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D.
Area/Force
Solution
Young's modulus (E) is defined as the ratio of stress to strain.
Correct Answer: A — Stress/Strain
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Q. What is the relationship between bulk modulus and compressibility?
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A.
Bulk modulus is the inverse of compressibility
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B.
Bulk modulus is equal to compressibility
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C.
Bulk modulus is the square of compressibility
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D.
There is no relationship
Solution
Bulk modulus is defined as the reciprocal of compressibility, indicating how incompressible a material is.
Correct Answer: A — Bulk modulus is the inverse of compressibility
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Q. What is the relationship between shear modulus (G) and Young's modulus (E)?
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A.
G = E / (2(1 + ν))
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B.
G = E * (2(1 + ν))
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C.
G = E / (1 + ν)
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D.
G = E * (1 + ν)
Solution
The relationship is given by G = E / (2(1 + ν)), where ν is Poisson's ratio.
Correct Answer: A — G = E / (2(1 + ν))
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Q. What is the relationship between shear modulus and Young's modulus for isotropic materials?
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A.
G = E/2(1 + ν)
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B.
G = E(1 + ν)/2
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C.
G = E/3
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D.
G = 2E
Solution
The shear modulus (G) is related to Young's modulus (E) and Poisson's ratio (ν) by the formula G = E/2(1 + ν).
Correct Answer: A — G = E/2(1 + ν)
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Q. What is the relationship between shear modulus and Young's modulus?
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A.
They are equal
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B.
Shear modulus is always greater
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C.
Shear modulus is less than Young's modulus
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D.
They are inversely proportional
Solution
Shear modulus is generally less than Young's modulus for most materials.
Correct Answer: C — Shear modulus is less than Young's modulus
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Q. What is the relationship between shear stress and shear strain in a material?
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A.
Shear modulus
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B.
Bulk modulus
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C.
Young's modulus
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D.
Poisson's ratio
Solution
The relationship between shear stress and shear strain is defined by the shear modulus.
Correct Answer: A — Shear modulus
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Q. What is the relationship between stress and strain in the elastic region of a material?
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A.
Stress is directly proportional to strain
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B.
Stress is inversely proportional to strain
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C.
Stress is independent of strain
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D.
Stress is proportional to the square of strain
Solution
In the elastic region, stress is directly proportional to strain, as described by Hooke's Law.
Correct Answer: A — Stress is directly proportional to strain
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Q. Which of the following describes Poisson's ratio?
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A.
Lateral strain / Longitudinal strain
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B.
Longitudinal strain / Lateral strain
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C.
Stress / Strain
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D.
Strain / Stress
Solution
Poisson's ratio (ν) is defined as the ratio of lateral strain to longitudinal strain.
Correct Answer: A — Lateral strain / Longitudinal strain
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Q. Which of the following is NOT a type of elastic deformation?
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A.
Tensile deformation
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B.
Compressive deformation
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C.
Shear deformation
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D.
Plastic deformation
Solution
Plastic deformation is not elastic; it is permanent deformation that occurs beyond the elastic limit.
Correct Answer: D — Plastic deformation
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Q. Which of the following is NOT a type of modulus of elasticity?
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A.
Young's modulus
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B.
Shear modulus
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C.
Bulk modulus
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D.
Tensile modulus
Solution
Tensile modulus is not a standard term; the correct terms are Young's modulus, shear modulus, and bulk modulus.
Correct Answer: D — Tensile modulus
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Q. Which of the following is NOT a type of stress?
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A.
Tensile stress
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B.
Compressive stress
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C.
Shear stress
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D.
Thermal stress
Solution
Thermal stress is a result of temperature changes, while tensile, compressive, and shear stresses are types of mechanical stress.
Correct Answer: D — Thermal stress
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Q. Which of the following is true about elastic potential energy stored in a stretched wire?
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A.
It is proportional to the square of the elongation
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B.
It is proportional to the elongation
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C.
It is independent of the elongation
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D.
It is inversely proportional to the elongation
Solution
The elastic potential energy stored in a stretched wire is given by U = (1/2) * Y * (ΔL^2 / L), which is proportional to the square of the elongation.
Correct Answer: A — It is proportional to the square of the elongation
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Q. Which of the following materials has the highest Young's modulus?
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A.
Rubber
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B.
Steel
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C.
Wood
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D.
Plastic
Solution
Steel has a much higher Young's modulus compared to rubber, wood, and plastic, indicating it is much stiffer.
Correct Answer: B — Steel
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