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Shear modulus or modulus of rigidity is
- a)the ratio of shearing stress to the corresponding lateral strain
- b)the ratio of shearing stress to the corresponding shearing strain
- c)the ratio of longitudinal stress to the corresponding shearing strain
- d)the ratio of shearing strain to the corresponding shearing stress
Correct answer is option 'B'. Can you explain this answer?
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Shear modulus or modulus of rigidity isa)the ratio of shearing stress ...
Shear modulus or modulus of rigidity is the ratio of shearing stress to the corresponding shearing strain, by the definition of shear modulus.
Most Upvoted Answer
Shear modulus or modulus of rigidity isa)the ratio of shearing stress ...
The correct answer is option 'B', which states that the shear modulus or modulus of rigidity is the ratio of shearing stress to the corresponding shearing strain. Let's understand this concept in detail:
Shear Modulus or Modulus of Rigidity Definition:
The shear modulus or modulus of rigidity is a material property that measures its resistance to shearing deformation. It determines the stiffness of a material under shear stress. The shear modulus is denoted by the symbol G.
Shear Stress and Shearing Strain:
Before understanding the shear modulus, it is important to know the terms shear stress and shearing strain:
1. Shear Stress:
Shear stress is the force exerted parallel to an area, divided by the normal area of the material. It is a measure of the intensity of the internal resistance within a material to resist deformation by shear. Shear stress is denoted by the symbol τ (tau).
2. Shearing Strain:
Shearing strain is the change in shape of a material when subjected to a shearing force. It represents the relative displacement between two adjacent layers of the material parallel to the direction of the applied shearing force. Shearing strain is denoted by the symbol γ (gamma).
Relation between Shear Stress and Shearing Strain:
The shear modulus is defined as the ratio of shear stress (τ) to the corresponding shearing strain (γ). Mathematically, it is represented as:
G = τ / γ
Where:
G = Shear Modulus or Modulus of Rigidity
τ = Shear Stress
γ = Shearing Strain
Explanation of the Correct Answer:
Option 'B' states that the shear modulus is the ratio of shearing stress to the corresponding shearing strain. This is the correct answer because it accurately represents the definition and formula of the shear modulus. The shear modulus is a material property that quantifies the resistance of a material to shearing deformation. It relates the shear stress and shearing strain, and the ratio of these two quantities represents the shear modulus.
Shear Modulus or Modulus of Rigidity Definition:
The shear modulus or modulus of rigidity is a material property that measures its resistance to shearing deformation. It determines the stiffness of a material under shear stress. The shear modulus is denoted by the symbol G.
Shear Stress and Shearing Strain:
Before understanding the shear modulus, it is important to know the terms shear stress and shearing strain:
1. Shear Stress:
Shear stress is the force exerted parallel to an area, divided by the normal area of the material. It is a measure of the intensity of the internal resistance within a material to resist deformation by shear. Shear stress is denoted by the symbol τ (tau).
2. Shearing Strain:
Shearing strain is the change in shape of a material when subjected to a shearing force. It represents the relative displacement between two adjacent layers of the material parallel to the direction of the applied shearing force. Shearing strain is denoted by the symbol γ (gamma).
Relation between Shear Stress and Shearing Strain:
The shear modulus is defined as the ratio of shear stress (τ) to the corresponding shearing strain (γ). Mathematically, it is represented as:
G = τ / γ
Where:
G = Shear Modulus or Modulus of Rigidity
τ = Shear Stress
γ = Shearing Strain
Explanation of the Correct Answer:
Option 'B' states that the shear modulus is the ratio of shearing stress to the corresponding shearing strain. This is the correct answer because it accurately represents the definition and formula of the shear modulus. The shear modulus is a material property that quantifies the resistance of a material to shearing deformation. It relates the shear stress and shearing strain, and the ratio of these two quantities represents the shear modulus.
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Shear modulus or modulus of rigidity isa)the ratio of shearing stress to the corresponding lateral strainb)the ratio of shearing stress to the corresponding shearing strainc)the ratio of longitudinal stress to the corresponding shearing straind)the ratio of shearing strain to the corresponding shearing stressCorrect answer is option 'B'. Can you explain this answer?
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