Youngs modulus, bulk modulus, modulus of rigidity - Question Bank

1. Stress is defined as force per unit:
A) Volume
B) Area
C) Length
D) Displacement
2. Which of the following is a dimensionless quantity?
A) Young's modulus
B) Bulk modulus
C) Modulus of rigidity
D) Strain
3. For an elastic material, it is known that Y > B > G. This implies:
A) Poisson's ratio is close to 0.5.
B) Poisson's ratio is close to 0.
C) The material is highly compressible.
D) The material has low resistance to shear.
4. What is the bulk modulus of a material if Y = 200 GPa and σ = 0.25?
A) 133.33 GPa
B) 166.67 GPa
C) 100 GPa
D) 200 GPa
5. A material has Y = 120 GPa and σ = 0.3. What is its shear modulus?
A) 46.15 GPa
B) 60 GPa
C) 92.31 GPa
D) 100 GPa
6. If a wire is stretched such that its length increases by 0.1%, and its diameter decreases by 0.04%, what is the Poisson's ratio?
A) 0.4
B) 0.1
C) 0.04
D) 0.2
7. Which modulus is most directly related to the concept of strain energy density under tension?
A) Bulk modulus
B) Shear modulus
C) Young's modulus
D) Modulus of resilience
8. The strain energy stored per unit volume in a deformed elastic material is given by:
A) Stress * Strain
B) 0.5 * Stress * Strain
C) Stress / Strain
D) Strain / Stress
9. What happens to the volume of a body when it is subjected to a large shear stress?
A) It increases significantly.
B) It decreases significantly.
C) It changes negligibly.
D) It depends on Young's modulus.
10. If Y is Young's modulus, B is bulk modulus, and G is shear modulus, which relation is always true for isotropic materials?
A) Y = 3B(1 - 2σ)
B) G = Y / (2(1 + σ))
C) B = Y / (3(1 + σ))
D) Y = G(1 + σ)
11. For an isotropic material, the number of independent elastic constants is:
A) 1
B) 2
C) 3
D) 9
12. A block is pushed sideways, distorting its shape but not its volume. This deformation is directly related to:
A) Young's modulus
B) Bulk modulus
C) Modulus of rigidity
D) Tensile strength
13. When a gas is compressed, the relevant modulus is:
A) Young's modulus
B) Shear modulus
C) Bulk modulus
D) Modulus of elasticity
14. A rod is subjected to equal and opposite forces applied to its ends, causing it to stretch. This is a scenario for determining:
A) Bulk modulus
B) Shear modulus
C) Young's modulus
D) Compressibility
15. Which of the following is NOT a measure of elastic property of a solid?
A) Young's modulus
B) Bulk modulus
C) Modulus of rigidity
D) Tensile strength
16. If Poisson's ratio for a material is 0.2, what is the ratio of Young's modulus to bulk modulus?
A) 1.8
B) 3.0
C) 4.0
D) 5.0
17. For a material, Y = 200 GPa and G = 80 GPa. Calculate Poisson's ratio.
A) 0.25
B) 0.5
C) 0.3
D) 0.4
18. A 10 cm side cube is subjected to a shear stress of 100 MPa. The top face is displaced by 0.1 cm relative to the bottom face. Calculate the modulus of rigidity.
A) 10^10 Pa
B) 10^11 Pa
C) 10^9 Pa
D) 10^12 Pa
19. A sphere of volume 1 m³ is submerged in a liquid and the pressure increases by 10^7 Pa. The volume decreases by 0.01 m³. What is the bulk modulus of the sphere material?
A) 10^9 Pa
B) 10^10 Pa
C) 10^11 Pa
D) 10^12 Pa
20. A steel wire of length 1 m and cross-sectional area 1 mm² is stretched by 1 mm by a force of 200 N. What is the Young's modulus of steel?
A) 2 x 10^11 Pa
B) 2 x 10^10 Pa
C) 2 x 10^12 Pa
D) 2 x 10^9 Pa
21. Consider a cube of side 'a'. If a tangential force F is applied to the top face, causing it to shift by 'x', what is the shear strain?
A) x/a
B) F/a^2
C) a/x
D) F/x
22. Which of the following statements is true for an elastic material?
A) Young's modulus is always greater than bulk modulus.
B) Bulk modulus is always greater than shear modulus.
C) Young's modulus is always greater than shear modulus.
D) The relationship between the moduli depends on the material's properties.
23. What is the compressibility of a substance with a bulk modulus of 2 x 10^11 Pa?
A) 0.5 x 10^-11 Pa^-1
B) 2 x 10^-11 Pa^-1
C) 5 x 10^10 Pa^-1
D) 0.5 x 10^11 Pa^-1
24. Compressibility is the reciprocal of which modulus?
A) Young's modulus
B) Shear modulus
C) Bulk modulus
D) Tensile modulus
25. When a solid is subjected to uniform pressure, its volume decreases. This property is related to which modulus?
A) Young's modulus
B) Shear modulus
C) Bulk modulus
D) Modulus of elasticity
26. If a material is stretched, its volume:
A) Increases
B) Decreases
C) May increase or decrease depending on Poisson's ratio
D) Remains constant if it's incompressible
27. What is the relationship between bulk modulus (B) and Young's modulus (Y) in terms of Poisson's ratio (σ)?
A) B = Y / (3(1 - 2σ))
B) B = Y / (1 - 2σ)
C) B = 3Y / (1 - 2σ)
D) B = Y / (3(1 + σ))
28. What is the relationship between Young's modulus (Y) and shear modulus (G) in terms of Poisson's ratio (σ)?
A) Y = 2G(1 + σ)
B) Y = G(1 + σ)
C) Y = 2G(1 - σ)
D) Y = G(1 - σ)
29. For an isotropic elastic material, the theoretical upper limit for Poisson's ratio is:
A) 0
B) 0.5
C) 1
D) 2
30. What is the value of Poisson's ratio (σ) if the lateral strain is zero for a given tensile strain?
A) 0
B) 0.5
C) 1
D) Undefined
31. What is the relationship between Young's modulus (Y), bulk modulus (B), and shear modulus (G) for an isotropic material?
A) Y = 9BG / (3B + G)
B) Y = 3BG / (B + G)
C) Y = 3BG / (3B + G)
D) Y = 9BG / (B + G)
32. If a material is incompressible, what is its bulk modulus?
A) Zero
B) Infinite
C) Equal to Young's modulus
D) Equal to shear modulus
33. Which elastic modulus is most relevant for understanding how a solid object deforms when a force is applied parallel to one of its surfaces?
A) Bulk modulus
B) Young's modulus
C) Modulus of rigidity
D) Compressibility
34. Which elastic modulus is most relevant for understanding how a submarine resists crushing at depth?
A) Young's modulus
B) Bulk modulus
C) Shear modulus
D) Modulus of elasticity
35. Which elastic modulus is most relevant for understanding the behavior of a spring?
A) Bulk modulus
B) Shear modulus
C) Young's modulus
D) None of the above
36. For most materials, the order of magnitude of the three elastic moduli is typically:
A) Y > B > G
B) G > B > Y
C) B > Y > G
D) Y ≈ B ≈ G
37. A material with a high modulus of rigidity will:
A) Compress easily
B) Stretch easily
C) Resist deformation of shape
D) Undergo large volume changes
38. What are the units of the modulus of rigidity in the SI system?
A) Pascal (Pa)
B) Newton (N)
C) Radian (rad)
D) Joule (J)
39. If a tangential force F is applied to the surface of a body of area A, causing a displacement x parallel to the force and perpendicular to the height h, what is the expression for the modulus of rigidity (G)?
A) G = (F * h) / (A * x)
B) G = (F * x) / (A * h)
C) G = (A * h) / (F * x)
D) G = (F * A) / (x * h)
40. The modulus of rigidity is defined as the ratio of:
A) Normal stress to volumetric strain
B) Shear stress to shear strain
C) Tensile stress to linear strain
D) Pressure to volume change
41. What does the modulus of rigidity (G), also known as shear modulus, measure?
A) Resistance to volume change
B) Resistance to elongation or compression
C) Resistance to shape change without volume change
D) The elasticity of a fluid
42. A substance with a very low bulk modulus is:
A) Very stiff
B) Easily compressible
C) Resistant to shape change
D) Strong under tension
43. What are the units of bulk modulus in the SI system?
A) Pascal (Pa)
B) Newton (N)
C) Meter (m)
D) Dyne/cm²
44. The formula for bulk modulus (B) is B = - (Pressure Change) / (Volumetric Strain). If a substance's volume changes by ΔV due to a pressure change ΔP, and its initial volume is V, what is the expression for bulk modulus?
A) B = - (ΔP * V) / ΔV
B) B = - (ΔV * V) / ΔP
C) B = - (ΔP * ΔV) / V
D) B = - ΔV / (ΔP * V)
45. Bulk modulus is defined as the ratio of:
A) Shear stress to shear strain
B) Tensile stress to tensile strain
C) Normal stress to volumetric strain
D) Volumetric stress to linear strain
46. What does bulk modulus (B) quantify?
A) Resistance to stretching or compression along an axis
B) Resistance to shape change without volume change
C) Resistance to volume change under uniform pressure
D) The maximum stress a material can withstand before permanent deformation
47. A material with a high Young's modulus is considered to be:
A) Highly ductile
B) Very elastic and stiff
C) Easily compressible
D) Prone to permanent deformation
48. What are the units of Young's modulus in the SI system?
A) Pascal (Pa)
B) Newton (N)
C) Meter (m)
D) Joule (J)
49. The formula for Young's modulus (Y) is given by Y = Stress / Strain. If a wire of length L and cross-sectional area A is stretched by a force F, resulting in an extension x, what is the expression for Young's modulus?
A) Y = (F * L) / (A * x)
B) Y = (F * x) / (A * L)
C) Y = (A * L) / (F * x)
D) Y = (F * A) / (L * x)
50. Which type of stress is primarily involved when calculating Young's modulus?
A) Shear stress
B) Compressive stress
C) Tensile stress
D) Tensile or compressive stress
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