Elasticity
Q. A cylindrical rod is subjected to a tensile force. If the diameter of the rod is doubled while keeping the length constant, what happens to the stress in the rod?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Stress is defined as force per unit area. Doubling the diameter increases the area by a factor of four, thus reducing the stress.
Correct Answer: B — Decreases
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Q. A cylindrical rod is subjected to a tensile force. If the radius of the rod is halved while keeping the length constant, how does the tensile stress change?
A.
It doubles
B.
It halves
C.
It quadruples
D.
It remains the same
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Solution
Tensile stress is given by force/area. Halving the radius reduces the area by a factor of four, thus the stress quadruples for the same force.
Correct Answer: C — It quadruples
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Q. A material has a bulk modulus of 200 GPa. If the pressure applied to it is increased by 50 MPa, what is the fractional change in volume?
A.
0.00025
B.
0.0005
C.
0.0025
D.
0.005
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Solution
The fractional change in volume is given by ΔV/V = ΔP/B. Here, ΔP = 50 MPa = 0.05 GPa, so ΔV/V = 0.05/200 = 0.00025.
Correct Answer: A — 0.00025
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Q. A material has a bulk modulus of 200 GPa. If the pressure on the material is increased by 10 MPa, what is the fractional change in volume?
A.
0.00005
B.
0.0001
C.
0.0002
D.
0.00025
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Solution
The fractional change in volume ΔV/V is given by ΔV/V = ΔP/B, where ΔP = 10 MPa and B = 200 GPa, resulting in 0.00005.
Correct Answer: B — 0.0001
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Q. A material has a bulk modulus of 200 GPa. What is the change in volume when a pressure of 50 MPa is applied?
A.
0.0125%
B.
0.025%
C.
0.05%
D.
0.1%
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Solution
The change in volume ΔV/V = P/B, so ΔV/V = 50 MPa / 200 GPa = 0.025%.
Correct Answer: B — 0.025%
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Q. A material has a Poisson's ratio of 0.3. What is the ratio of lateral strain to longitudinal strain?
A.
0.3
B.
0.7
C.
1.0
D.
0.5
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Solution
Poisson's ratio is defined as the negative ratio of lateral strain to longitudinal strain, so a Poisson's ratio of 0.3 means the ratio is 0.3.
Correct Answer: A — 0.3
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Q. A material is said to be elastic if it:
A.
Returns to its original shape after deformation
B.
Can be permanently deformed
C.
Breaks under stress
D.
Has a high tensile strength
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Solution
A material is considered elastic if it returns to its original shape after the removal of the applied stress.
Correct Answer: A — Returns to its original shape after deformation
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Q. A material is subjected to a tensile stress of 100 MPa and experiences a strain of 0.002. What is its Young's modulus?
A.
50 GPa
B.
100 GPa
C.
200 GPa
D.
500 GPa
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Solution
Young's modulus (Y) = Stress / Strain = 100 MPa / 0.002 = 50 GPa.
Correct Answer: B — 100 GPa
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Q. A material with a Poisson's ratio of 0.5 is considered to be:
A.
Perfectly elastic
B.
Perfectly plastic
C.
Incompressible
D.
Brittle
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Solution
A Poisson's ratio of 0.5 indicates that the material is incompressible.
Correct Answer: C — Incompressible
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Q. A spring obeys Hooke's law. If the spring constant is doubled, what happens to the elongation for the same applied force?
A.
Elongation doubles
B.
Elongation halves
C.
Elongation remains the same
D.
Elongation quadruples
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Solution
According to Hooke's law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.
Correct Answer: B — Elongation halves
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Q. A spring stretches 5 cm when a load of 10 N is applied. What is the spring constant?
A.
200 N/m
B.
100 N/m
C.
50 N/m
D.
25 N/m
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Solution
Using Hooke's law, k = F/x = 10 N / 0.05 m = 200 N/m.
Correct Answer: B — 100 N/m
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Q. A wire of length L and cross-sectional area A is stretched by a force F. If the Young's modulus of the material is Y, what is the extension of the wire?
A.
F * L / (A * Y)
B.
A * Y * L / F
C.
F * A / (Y * L)
D.
Y * L / (F * A)
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Solution
The extension of the wire can be calculated using the formula: extension = (F * L) / (A * Y).
Correct Answer: A — F * L / (A * Y)
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Q. A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation ΔL?
A.
ΔL = FL / (AE)
B.
ΔL = AE / (FL)
C.
ΔL = EFL / A
D.
ΔL = A / (FL)
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Solution
The elongation ΔL of a wire is given by ΔL = FL / (AE), where E is Young's modulus.
Correct Answer: A — ΔL = FL / (AE)
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Q. A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation of the wire?
A.
ΔL = (F * L) / (A * Y)
B.
ΔL = (Y * F) / (A * L)
C.
ΔL = (A * Y) / (F * L)
D.
ΔL = (F * A) / (Y * L)
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Solution
The elongation ΔL of a wire is given by ΔL = (F * L) / (A * Y), where Y is Young's modulus.
Correct Answer: A — ΔL = (F * L) / (A * Y)
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Q. If a material exhibits a linear stress-strain relationship, what type of material is it likely to be?
A.
Brittle material
B.
Ductile material
C.
Elastic material
D.
Plastic material
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Solution
A linear stress-strain relationship indicates that the material behaves elastically within the limit of proportionality.
Correct Answer: C — Elastic material
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Q. If a material exhibits plastic deformation, which of the following is true?
A.
It returns to its original shape after the load is removed
B.
It does not return to its original shape after the load is removed
C.
It behaves like a perfect elastic material
D.
It has a very high Young's modulus
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Solution
Plastic deformation means that the material does not return to its original shape after the load is removed.
Correct Answer: B — It does not return to its original shape after the load is removed
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Q. If a material has a high shear modulus, what does it imply about the material?
A.
It is very flexible
B.
It is very stiff against shear forces
C.
It is very brittle
D.
It is very ductile
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Solution
A high shear modulus indicates that the material is very stiff and resists shear deformation.
Correct Answer: B — It is very stiff against shear forces
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Q. If a material has a Poisson's ratio of 0.3, what does this imply about its behavior under stress?
A.
It expands laterally
B.
It contracts laterally
C.
It does not change shape
D.
It becomes brittle
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Solution
A Poisson's ratio of 0.3 indicates that the material will contract laterally when stretched.
Correct Answer: B — It contracts laterally
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Q. If a material has a Poisson's ratio of 0.3, what does this imply about its lateral strain when subjected to axial strain?
A.
Lateral strain is equal to axial strain
B.
Lateral strain is 0.3 times the axial strain
C.
Lateral strain is 3 times the axial strain
D.
Lateral strain is independent of axial strain
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Solution
A Poisson's ratio of 0.3 means that the lateral strain is 0.3 times the axial strain.
Correct Answer: B — Lateral strain is 0.3 times the axial strain
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Q. If a material has a Poisson's ratio of 0.3, what does this imply?
A.
It expands laterally when stretched
B.
It contracts laterally when stretched
C.
It has no lateral strain
D.
It is incompressible
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Solution
A Poisson's ratio of 0.3 implies that the material contracts laterally when stretched.
Correct Answer: B — It contracts laterally when stretched
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Q. If a material has a Young's modulus of 200 GPa, what does this indicate?
A.
It is very elastic
B.
It is very brittle
C.
It is very ductile
D.
It is very plastic
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Solution
A high Young's modulus indicates that the material is very elastic.
Correct Answer: A — It is very elastic
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Q. If a material is stretched beyond its elastic limit, what happens?
A.
It returns to its original shape
B.
It undergoes permanent deformation
C.
It becomes stronger
D.
It becomes weaker
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Solution
When a material is stretched beyond its elastic limit, it undergoes permanent deformation and does not return to its original shape.
Correct Answer: B — It undergoes permanent deformation
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Q. If a wire is stretched and its length increases by 2%, what is the strain?
A.
0.02
B.
0.2
C.
2
D.
200
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Solution
Strain is defined as the change in length divided by the original length, so 2% = 0.02.
Correct Answer: A — 0.02
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Q. If a wire of length L and cross-sectional area A is stretched by a force F, what is the expression for the elongation?
A.
F * L / (A * E)
B.
A * F / (L * E)
C.
E * F / (A * L)
D.
L * E / (A * F)
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Solution
The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).
Correct Answer: A — F * L / (A * E)
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Q. If the length of a wire is doubled while keeping the cross-sectional area constant, how does its Young's modulus change?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Young's modulus is a material property and does not change with the dimensions of the wire.
Correct Answer: C — It remains the same
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Q. If the strain in a material is 0.01 and the Young's modulus is 150 GPa, what is the stress?
A.
1.5 MPa
B.
15 MPa
C.
150 MPa
D.
1500 MPa
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Solution
Stress = Young's modulus × Strain = 150 GPa × 0.01 = 150 MPa.
Correct Answer: C — 150 MPa
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Q. If the stress applied to a material is doubled, what happens to the strain if the material behaves elastically?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
According to Hooke's Law, if stress is doubled, strain also doubles for elastic materials.
Correct Answer: A — It doubles
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Q. If the temperature of a material increases, what happens to its Young's modulus?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Depends on the material
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Solution
Generally, the Young's modulus of materials decreases with an increase in temperature.
Correct Answer: B — Decreases
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Q. If the Young's modulus of a material is 100 GPa and it is subjected to a tensile stress of 200 MPa, what is the strain produced?
A.
0.002
B.
0.0025
C.
0.01
D.
0.005
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Solution
Strain = Stress / Young's modulus = 200 MPa / 100 GPa = 0.002.
Correct Answer: A — 0.002
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Q. In a material, if the strain energy density is given by U, what is the expression for the total strain energy stored in a volume V of the material?
A.
U * V
B.
U / V
C.
U + V
D.
U - V
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Solution
The total strain energy stored in a volume V is given by the product of strain energy density U and volume V, i.e., Total Energy = U * V.
Correct Answer: A — U * V
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